1 Development of UHVDC transmission capabilities The economical development of China is closely connected with safe and reliable power supply.Load centers e.g.in central and eastern China need huge amounts of electric...1 Development of UHVDC transmission capabilities The economical development of China is closely connected with safe and reliable power supply.Load centers e.g.in central and eastern China need huge amounts of electrical power.Available energy resources and consumption areas are often distributed inverse.As a consequence it is necessary to import electrical power to load center areas in an economic and efficient way.展开更多
In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This s...In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This semi-analytic method has the advantage of overcoming the obstacle of the hardest nonlinear terms and is used to explain the origin of the bright and dark soliton solutions through the Schrödinger equation in its non-local form and the Radhakrishnan-Kundu-Laksmannan (RKL) equation. Numerical examples demonstrate the effectiveness of this method.展开更多
Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a num...Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a number of track parameters.One possible reason for deviations between simulated and measured results for the dynamic track behaviour is the uncertainty of the value of some track parameters used as input for the simulation.This in turn results in an uncertainty in the simulation results.In this contribution,it is proposed to use the general transformation method to assess a uncertainty band for the results.Most relevant input parameters for determining the point input mobility and the track decay rate for a ballasted track are analysed with regard to the uncertainties and for the value of each an interval is determined.Then,the general transformation method is applied to four different simulation methods,working both in the frequency and time domains.For one example track,the resulting uncertainty bands are compared to one dataset with measurements for the point mobility and the track decay rate.In addition,a sensitivity analysis is performed to determine the parameters that significantly influence the overall result.While all four simulation methods produce broad uncertainty bands for the results,none did match the measured results for the point mobility and the track decay rate over the entire frequency range considered.Besides the large influence of the uncertain pad stiffness,it turned out that the rail wear is also a significant source of uncertainty of the results.Overall,it is demonstrated that the proposed approach allows assessing the influence of uncertain input parameters in detail.展开更多
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
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
In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to ana...In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.展开更多
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on t...We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.展开更多
A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equati...A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.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
Aiming at the existing problems of discrete cosine transform(DCT) de-noising method, we introduce the idea of wavelet neighboring coefficients(WNC) de-noising method, and propose the cosine neighboring coefficients(CN...Aiming at the existing problems of discrete cosine transform(DCT) de-noising method, we introduce the idea of wavelet neighboring coefficients(WNC) de-noising method, and propose the cosine neighboring coefficients(CNC) de-noising method. Based on DCT, a novel method for the fault feature extraction of hydraulic pump is analyzed. The vibration signal of pump is de-noised with CNC de-noising method, and the fault feature is extracted by performing Hilbert-Huang transform(HHT) to the output signal. The analysis results of the simulation signal and the actual one demonstrate that the proposed CNC de-noising method and the fault feature extraction method have more superior ability than the traditional ones.展开更多
In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easi...In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.展开更多
Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process...Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis.展开更多
In the context of the transformation method, we propose a general approach to construct numerically the mapping generated by imposing specific boundary conditions with a targeted function, and the necessary material a...In the context of the transformation method, we propose a general approach to construct numerically the mapping generated by imposing specific boundary conditions with a targeted function, and the necessary material and heat source spatial distributions are then derived with the help of transformation method. The construction of mapping by grid generation method through solving partial differential equations circumvents the limitation of device geometry, which paves the way for designing more complex heat flow control devices. Two numerical examples are also given to show how to design material properties and heat source in order to control temperature patterns.展开更多
Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for examp...Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for example,a long porous slider and a circular porous slider.By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method.Solutions are obtained for different values of Reynolds numbers,velocity slip,and magnetic field.We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long and circular sliders,whereas the magnetic effect is also noticeable.展开更多
An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with interm...An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.展开更多
An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of...An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact Dower series solution.展开更多
In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,th...In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution.展开更多
The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been s...The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.展开更多
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Ko...By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.展开更多
文摘1 Development of UHVDC transmission capabilities The economical development of China is closely connected with safe and reliable power supply.Load centers e.g.in central and eastern China need huge amounts of electrical power.Available energy resources and consumption areas are often distributed inverse.As a consequence it is necessary to import electrical power to load center areas in an economic and efficient way.
文摘In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This semi-analytic method has the advantage of overcoming the obstacle of the hardest nonlinear terms and is used to explain the origin of the bright and dark soliton solutions through the Schrödinger equation in its non-local form and the Radhakrishnan-Kundu-Laksmannan (RKL) equation. Numerical examples demonstrate the effectiveness of this method.
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
文摘Rolling noise is an important source of railway noise and depends also on the dynamic behaviour of a railway track.This is characterized by the point or transfer mobility and the track decay rate,which depend on a number of track parameters.One possible reason for deviations between simulated and measured results for the dynamic track behaviour is the uncertainty of the value of some track parameters used as input for the simulation.This in turn results in an uncertainty in the simulation results.In this contribution,it is proposed to use the general transformation method to assess a uncertainty band for the results.Most relevant input parameters for determining the point input mobility and the track decay rate for a ballasted track are analysed with regard to the uncertainties and for the value of each an interval is determined.Then,the general transformation method is applied to four different simulation methods,working both in the frequency and time domains.For one example track,the resulting uncertainty bands are compared to one dataset with measurements for the point mobility and the track decay rate.In addition,a sensitivity analysis is performed to determine the parameters that significantly influence the overall result.While all four simulation methods produce broad uncertainty bands for the results,none did match the measured results for the point mobility and the track decay rate over the entire frequency range considered.Besides the large influence of the uncertain pad stiffness,it turned out that the rail wear is also a significant source of uncertainty of the results.Overall,it is demonstrated that the proposed approach allows assessing the influence of uncertain input parameters in detail.
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.
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The project partly supported by the Foundation of Zhongshan University Advanced Research Center
文摘In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.
文摘We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the （3＋1）-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics.
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.
基金the National Natural Science Foundation of China(No.51275524)the General Armaments Department Equipment Support Research Project
文摘Aiming at the existing problems of discrete cosine transform(DCT) de-noising method, we introduce the idea of wavelet neighboring coefficients(WNC) de-noising method, and propose the cosine neighboring coefficients(CNC) de-noising method. Based on DCT, a novel method for the fault feature extraction of hydraulic pump is analyzed. The vibration signal of pump is de-noised with CNC de-noising method, and the fault feature is extracted by performing Hilbert-Huang transform(HHT) to the output signal. The analysis results of the simulation signal and the actual one demonstrate that the proposed CNC de-noising method and the fault feature extraction method have more superior ability than the traditional ones.
文摘In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.
基金the National High.Technology Research and Development Programme of China(2004AA404013)
文摘Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis.
基金supported by the National Natural Science Foundation of China(Nos.11372035,10832002 and 11221202)China Postdoctoral Science Foundation(No.2014M550054)
文摘In the context of the transformation method, we propose a general approach to construct numerically the mapping generated by imposing specific boundary conditions with a targeted function, and the necessary material and heat source spatial distributions are then derived with the help of transformation method. The construction of mapping by grid generation method through solving partial differential equations circumvents the limitation of device geometry, which paves the way for designing more complex heat flow control devices. Two numerical examples are also given to show how to design material properties and heat source in order to control temperature patterns.
文摘Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for example,a long porous slider and a circular porous slider.By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method.Solutions are obtained for different values of Reynolds numbers,velocity slip,and magnetic field.We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long and circular sliders,whereas the magnetic effect is also noticeable.
基金Project supported by the National Basic Research Program of China(973 Program)(No.2011CB013800)
文摘An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution.
基金Project supported by the National Natural Science Foundation of China(Nos.50909017,51109031, 50921001,11072053,and 51009022)the Doctoral Foundation of Ministry of Education of China(No.20100041120037)+1 种基金the Fundamental Research Funds for the Central Universities (Nos.DUT12LK52 and DUT12LK34)the Major State Basic Research Development Program of China(973 Program)(Nos.2010CB832704 and 2013CB036101)
文摘An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact Dower series solution.
基金funded by National Natural Science Foundation of China(No.11471215)。
文摘In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution.
基金supported by the National Natural Science Foundation of China (90916007 and 91116008)
文摘The transformation method to control waves has received widespread attention in electromagnetism and acoustics. However, this machinery is not directly applicable to the control of elastic waves, because it has been shown that the Navier＇s equation does not usually retain its form under coordinate transformation. In this letter, we prove the form invariance of the Navier＇s equation under the conformal mapping based on the Helmholtz decomposition method. The needed material parameters are provided to manipulate elastic waves. The validity of this approach is confirmed by an active stealth device which can disguise the signal source by changing its position. Experimental verifications and potential applications may be expected in nondestructive testing, structural seismic design and other fields.
基金Supported by National Natural Science Foundation of China under Grant No.71171035
文摘By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
