This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence ...This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.展开更多
This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomati...This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.展开更多
In this study,the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method.The parametric studies reveal that porosity enhances the...In this study,the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method.The parametric studies reveal that porosity enhances the fin heat dissipating capacity but the internal heat generation decreases the heat enhancement capacity of extended surface.Also,it is established that when the internal heat parameter increases to some certain values,some negative effects are recorded where the fin stores heat rather than dissipating it.This scenario defeats the prime purpose of the cooling fin.Additionally,it is established in the present study that the limiting value of porosity parameter for thermal stability for the passive device increases as internal heat parameter increases.This shows that although the internal heat parameter can help assist higher range and value of thermal stability of the fin,it produces negative effect which greatly defeats the ultimate purpose of the fin.The results in the work will help in fin design for industrial applications where internal heat generation is involved.展开更多
We give a study on the general Moiler transformation and emphatically introduce its differential form. In this paper, a definition of acceleration is given in spacetime language and the inertial reference frame is als...We give a study on the general Moiler transformation and emphatically introduce its differential form. In this paper, a definition of acceleration is given in spacetime language and the inertial reference frame is also settled. With a discussion of the geodesic equations of motion, the differential form of the general MФller transformation at arbitrary direction is presented.展开更多
Different fragments of a hot-rolled and homogenized Cu–Zn–Al shape memory alloy（SMA） were subjected to thermal cycling by means of a differential scanning calorimetric（DSC） device. During thermal cycling, heatin...Different fragments of a hot-rolled and homogenized Cu–Zn–Al shape memory alloy（SMA） were subjected to thermal cycling by means of a differential scanning calorimetric（DSC） device. During thermal cycling, heating was performed at the same constant rate of increasing temperature while cooling was carried out at different rates of decreasing temperature. For each cooling rate, the temperature decreased in the same thermal interval. During each cooling stage, an exothermic peak（maximum） was observed on the DSC thermogram. This peak was associated with forward martensitic transformation. The DSC thermograms were analyzed with PROTEUS software： the critical martensitic transformation start（Ms） and finish（Mf） temperatures were determined by means of integral and tangent methods, and the dissipated heat was evaluated by the area between the corresponding maximum plot and a sigmoid baseline. The effects of the increase in cooling rate, assessed from a calorimetric viewpoint, consisted in the augmentation of the exothermic peak and the delay of direct martensitic transformation. The latter had the tendency to move to lower critical transformation temperatures. The martensite plates changed in morphology by becoming more oriented and by an augmenting in surface relief, which corresponded with the increase in cooling rate as observed by scanning electron microscopy（SEM） and atomic force microscopy（AFM）.展开更多
The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results sh...The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results show that DTM is an efficient and accurate technique for finding exact and approximate solutions.展开更多
Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy,low friction,low noise and high stability.The rotor system with axial-grooved gas-lubricated jo...Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy,low friction,low noise and high stability.The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system.The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail.The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory.A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing.The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method.The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system,and the dynamic equation of motion is calculated by the modified Wilson-0-based method.To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings,such as bifurcation and chaos,the bifurcation diagram,the orbit diagram,the Poincar6 map,the time series and the frequency spectrum are employed.The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena,such as the periodic,period-doubling,quasi-periodic,period-4 and chaotic motion,and so on.The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.展开更多
Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytical...Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytically using differential transformation method. Velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are determined analytically. The influence of pertinent parameters such as magnetic parameter, nanofluid volume fraction, viscosity parameter and Eckert number on the flow and heat transfer characteristics is discussed. Results indicate that skin friction coefficient decreases with increase of magnetic parameter, nanofluid volume fraction and viscosity parameter. Nusselt number increases with increase of magnetic parameter and nanofluid volume fraction while it decreases with increase of Eckert number and viscosity parameter.展开更多
The present work establishes an analytical model for computing the temperature distribution, fin efficiency and optimum design parameters of a constructal T-shaped porous fin operating in fully wet condition. For more...The present work establishes an analytical model for computing the temperature distribution, fin efficiency and optimum design parameters of a constructal T-shaped porous fin operating in fully wet condition. For more practical results, this study considers a cubic polynomial relationship between the humidity ratio of saturated air and the corresponding fin surface temperature. The temperature distribution has been determined by solving the highly non-linear governing equations using a semi-analytical transformation technique called Differential Transform Method. A comparison of the results with that of a numerical model shows that this transformation method is a very efficient and convenient tool for solution of non-linear problems. The effects of various geometric, thermo-physical and psychometric parameters on the temperature distribution, fin efficiency and optimum design condition have been investigated. Also, a comparison has been presented between solid and porous fins and the results point out that by selecting an appropriate value of porosity, the heat transfer rate can be increased than the corresponding solid fin.展开更多
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious...The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.展开更多
The primary goal of this study is to examine the flow of non-Newtonian Sutterby fluid conveying tiny particles as well as the induced magnetic field in the involvement of motile gyrotactic microorganisms.The flow is c...The primary goal of this study is to examine the flow of non-Newtonian Sutterby fluid conveying tiny particles as well as the induced magnetic field in the involvement of motile gyrotactic microorganisms.The flow is configured between a pair of circular disks filled with Sutterby fluid conveying tiny particles and gyrotactic microorganisms.The impact of Arrhenius kinetics and thermal radiation is also considered in the governing flow.The presented mathematical models are modified into nonlinear ordinary differential equations using the relevant similarity transformations.To compute the numerical solutions of nonlinear ordinary differential equations,the differential transform procedure(DTM)is used.For nonlinear problems,integral transform techniques are more difficult to execute.However,a polynomial solution is obtained as an analytical solution using the differential transform method,which is based on Taylor expansion.To improve the convergence of the formulated mathematical modeling,the Padéapproximation was combined with the differential transformation method.Variations of different dimensionless factors are discussed for velocity,temperature field,concentration distribution,and motile gyrotactic microorganism profile.Torque on both plates is calculated and presented through tables.展开更多
The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD bo...The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.展开更多
This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with...This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.展开更多
The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from ...The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.展开更多
The firing accuracy of a tank gun is affected significantly by the flexural motion of the barrel.For the purpose of satisfying the requirement of efficiently and accurately dynamic analysis and optimization of the tan...The firing accuracy of a tank gun is affected significantly by the flexural motion of the barrel.For the purpose of satisfying the requirement of efficiently and accurately dynamic analysis and optimization of the tank gun barrel to ensure it has good dynamic characteristics and firing accuracy,the high-fidelity dynamic model of a tank gun barrel is developed according to the transfer matrix method for multibody system which has features of high degree of stylization and high computational speed.The transfer matrix of the non-uniform Euler-Bernoulli beam(NU-EB beam)is deduced from governing differential equations of motion utilizing the differential transform method.The orthogonality of augmented eigenvectors for the NU-EB beam is proven which can be used for its exact dynamics response analysis using the modal method.In allusion to the tank gun barrel with non-uniform cross-section,the barrel is modeled as a combination of several uniform and non-uniform transverse vibrating Euler-Bernoulli beams.The overall transfer equation and matrix of the tank gun barrel are established according to the automatic deduction theorem of the overall transfer equation of multibody system.The present method is proven to be effective by comparing the computational results to those in published literatures.The vibration characteristics of a tank gun barrel with a non-uniform cross-section are analyzed accurately and are verified by the modal test.展开更多
In this paper,two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect...In this paper,two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function.Using the composite Boole's rule the distributedorder Bagley-Torvik equation is approximated by a multi-term time-fractional equation,which is then solved by the GrunwaldLetnikov method(GLM)and the fractional differential transform method(FDTM).Finally,we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.展开更多
In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr...In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.展开更多
In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-...In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.展开更多
文摘This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Natural Science Foundation of Jiangsu Province(No.SBK201140044)the Specialized Research Fund for Doctoral Program of Higher Education(No.20130002110044)
文摘This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.
文摘In this study,the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method.The parametric studies reveal that porosity enhances the fin heat dissipating capacity but the internal heat generation decreases the heat enhancement capacity of extended surface.Also,it is established that when the internal heat parameter increases to some certain values,some negative effects are recorded where the fin stores heat rather than dissipating it.This scenario defeats the prime purpose of the cooling fin.Additionally,it is established in the present study that the limiting value of porosity parameter for thermal stability for the passive device increases as internal heat parameter increases.This shows that although the internal heat parameter can help assist higher range and value of thermal stability of the fin,it produces negative effect which greatly defeats the ultimate purpose of the fin.The results in the work will help in fin design for industrial applications where internal heat generation is involved.
文摘We give a study on the general Moiler transformation and emphatically introduce its differential form. In this paper, a definition of acceleration is given in spacetime language and the inertial reference frame is also settled. With a discussion of the geodesic equations of motion, the differential form of the general MФller transformation at arbitrary direction is presented.
基金supported by the project PN-II-ID-PCE-2012-4-0033,contract 13/2013
文摘Different fragments of a hot-rolled and homogenized Cu–Zn–Al shape memory alloy（SMA） were subjected to thermal cycling by means of a differential scanning calorimetric（DSC） device. During thermal cycling, heating was performed at the same constant rate of increasing temperature while cooling was carried out at different rates of decreasing temperature. For each cooling rate, the temperature decreased in the same thermal interval. During each cooling stage, an exothermic peak（maximum） was observed on the DSC thermogram. This peak was associated with forward martensitic transformation. The DSC thermograms were analyzed with PROTEUS software： the critical martensitic transformation start（Ms） and finish（Mf） temperatures were determined by means of integral and tangent methods, and the dissipated heat was evaluated by the area between the corresponding maximum plot and a sigmoid baseline. The effects of the increase in cooling rate, assessed from a calorimetric viewpoint, consisted in the augmentation of the exothermic peak and the delay of direct martensitic transformation. The latter had the tendency to move to lower critical transformation temperatures. The martensite plates changed in morphology by becoming more oriented and by an augmenting in surface relief, which corresponded with the increase in cooling rate as observed by scanning electron microscopy（SEM） and atomic force microscopy（AFM）.
文摘The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results show that DTM is an efficient and accurate technique for finding exact and approximate solutions.
基金supported by National Natural Science Foundation of China(Grant No.51075327)National Key Basic Research and Development Program of China(973 Program,Grant No.2013CB035705)+3 种基金Shaanxi Provincial Natural Science Foundation of China(Grant No.2013JQ7008)Open Project of State Key Laboratory of Mechanical Transmission of China(Grant No.SKLMT-KFKT-201011)Tribology Science Fund of State Key Laboratory of Tribology of China(Grant No.SKLTKF11A02)Scientific Research Program of Shaanxi Provincial Education Department of China(Grant Nos.12JK0661,12JK0680)
文摘Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy,low friction,low noise and high stability.The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system.The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail.The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory.A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing.The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method.The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system,and the dynamic equation of motion is calculated by the modified Wilson-0-based method.To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings,such as bifurcation and chaos,the bifurcation diagram,the orbit diagram,the Poincar6 map,the time series and the frequency spectrum are employed.The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena,such as the periodic,period-doubling,quasi-periodic,period-4 and chaotic motion,and so on.The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.
文摘Kerosene-alumina nanofluid flow and heat transfer in the presence of magnetic field are studied. The basic partial differential equations are reduced to ordinary differential equations which are solved semi analytically using differential transformation method. Velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are determined analytically. The influence of pertinent parameters such as magnetic parameter, nanofluid volume fraction, viscosity parameter and Eckert number on the flow and heat transfer characteristics is discussed. Results indicate that skin friction coefficient decreases with increase of magnetic parameter, nanofluid volume fraction and viscosity parameter. Nusselt number increases with increase of magnetic parameter and nanofluid volume fraction while it decreases with increase of Eckert number and viscosity parameter.
文摘The present work establishes an analytical model for computing the temperature distribution, fin efficiency and optimum design parameters of a constructal T-shaped porous fin operating in fully wet condition. For more practical results, this study considers a cubic polynomial relationship between the humidity ratio of saturated air and the corresponding fin surface temperature. The temperature distribution has been determined by solving the highly non-linear governing equations using a semi-analytical transformation technique called Differential Transform Method. A comparison of the results with that of a numerical model shows that this transformation method is a very efficient and convenient tool for solution of non-linear problems. The effects of various geometric, thermo-physical and psychometric parameters on the temperature distribution, fin efficiency and optimum design condition have been investigated. Also, a comparison has been presented between solid and porous fins and the results point out that by selecting an appropriate value of porosity, the heat transfer rate can be increased than the corresponding solid fin.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
基金funded by“Taif University Researchers Supporting Project Number(TURSP-2020/16),Taif University,Taif,Saudi Arabia.”。
文摘The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.
文摘The primary goal of this study is to examine the flow of non-Newtonian Sutterby fluid conveying tiny particles as well as the induced magnetic field in the involvement of motile gyrotactic microorganisms.The flow is configured between a pair of circular disks filled with Sutterby fluid conveying tiny particles and gyrotactic microorganisms.The impact of Arrhenius kinetics and thermal radiation is also considered in the governing flow.The presented mathematical models are modified into nonlinear ordinary differential equations using the relevant similarity transformations.To compute the numerical solutions of nonlinear ordinary differential equations,the differential transform procedure(DTM)is used.For nonlinear problems,integral transform techniques are more difficult to execute.However,a polynomial solution is obtained as an analytical solution using the differential transform method,which is based on Taylor expansion.To improve the convergence of the formulated mathematical modeling,the Padéapproximation was combined with the differential transformation method.Variations of different dimensionless factors are discussed for velocity,temperature field,concentration distribution,and motile gyrotactic microorganism profile.Torque on both plates is calculated and presented through tables.
基金supported by the National Natural Science Foundation of China (Nos. 50936003 and 51076012)the Open Project of State Key Laboratory for Advanced Metals and Materials (No. 2009Z-02)
文摘The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.
基金Project supported by the National Natural Sciences Foundation of China(No.11272175)the Specialized Research Found for Doctoral Program of Higher Education(No.20130002110044)
文摘This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.
基金Project supported by the National Natural Sciences Foundation of China(No.11272175)the Specialized Research Found for Doctoral Program of Higher Education(No.20130002110044)
文摘The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.
基金This work was supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK20190438)the National Natural Science Foundation of China(Grant No.11902158).
文摘The firing accuracy of a tank gun is affected significantly by the flexural motion of the barrel.For the purpose of satisfying the requirement of efficiently and accurately dynamic analysis and optimization of the tank gun barrel to ensure it has good dynamic characteristics and firing accuracy,the high-fidelity dynamic model of a tank gun barrel is developed according to the transfer matrix method for multibody system which has features of high degree of stylization and high computational speed.The transfer matrix of the non-uniform Euler-Bernoulli beam(NU-EB beam)is deduced from governing differential equations of motion utilizing the differential transform method.The orthogonality of augmented eigenvectors for the NU-EB beam is proven which can be used for its exact dynamics response analysis using the modal method.In allusion to the tank gun barrel with non-uniform cross-section,the barrel is modeled as a combination of several uniform and non-uniform transverse vibrating Euler-Bernoulli beams.The overall transfer equation and matrix of the tank gun barrel are established according to the automatic deduction theorem of the overall transfer equation of multibody system.The present method is proven to be effective by comparing the computational results to those in published literatures.The vibration characteristics of a tank gun barrel with a non-uniform cross-section are analyzed accurately and are verified by the modal test.
文摘In this paper,two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function.Using the composite Boole's rule the distributedorder Bagley-Torvik equation is approximated by a multi-term time-fractional equation,which is then solved by the GrunwaldLetnikov method(GLM)and the fractional differential transform method(FDTM).Finally,we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.
基金Project supported by the Natural Science Foundation of Inner Mongolia of China (Grant No. 20080404MS0104)the Young Scientists Fund of Inner Mongolia University of China (Grant No. ND0811)
文摘In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.
文摘In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.
