In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)deriva...In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.展开更多
This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional ...This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.展开更多
In this paper,the density-independent fractional diffusion-reaction(FDR)equation involving quadratic nonlinearity is investigated.The fractional derivative is illustrated in the beta derivative sense.We firstly propos...In this paper,the density-independent fractional diffusion-reaction(FDR)equation involving quadratic nonlinearity is investigated.The fractional derivative is illustrated in the beta derivative sense.We firstly propose Bernoulli(G'/G)-expansion method to study nonlinear fractional differential equations(NFDEs).Subsequently,closed form solutions of the density-independent FDR equation are acquired successfully.In order to better understand the dynamic behaviors of these solutions,3D,contour map and line plots are given by the computer simulation.The results show that the proposed method is a reliable and efficient approach.展开更多
Two novel poly[(3-alkylthiophene-2,5-diyl)-(benzylidenequinomethane-2,5-diyl)s] derivatives, poly[ (3-butylthiophene-2,5-diyl)-( p-N,N-dimethylamino) benzylidenequinomethane-2,5-diyl) ] ( PBTDMABQ) and poly [( 3-octyl...Two novel poly[(3-alkylthiophene-2,5-diyl)-(benzylidenequinomethane-2,5-diyl)s] derivatives, poly[ (3-butylthiophene-2,5-diyl)-( p-N,N-dimethylamino) benzylidenequinomethane-2,5-diyl) ] ( PBTDMABQ) and poly [( 3-octylthiophene2,5-diyl) -(p-N, N-dimethylamino ) benzylidenequinomethane-2, 5-diyl)] (POTDMABQ), were synthesized.The band gaps of the two polymers are calculated as 1. 75 eV for PBTDMABQ and 1. 69 eV for POTDMABQ,respectively. The homogenous films of the two polymers were prepared and their third-ordernonlinear optical properties were studied by the backward degenerate four-wave mixing at 532 nm. Byusing the relative measurement technique, the third-order nonlinear optical susceptibilities ofPBTDMABQ and POTDMABQ are calculated as 5. 62 X 10^(-9) and 1. 22 X 10^(-8) ESU, respectively. It isfound that substituted alky groups have strong effects on the band gap and nonlinear opticalproperties of the two polymers. The relatively big third-order nonlinear optical susceptibilitiesand small band gap of POTDMABQ resulted mainly from the longer alkyl with strong electron-donatingability can enhance the delocation degree of conjugated π electronics.展开更多
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
TeOx-SiO2 composite films having third-order nonlinearities were prepared by electrochemically induced sol-gel deposition method on ITO substrate.The third-order optical nonlinearities of the films were measured by Z-...TeOx-SiO2 composite films having third-order nonlinearities were prepared by electrochemically induced sol-gel deposition method on ITO substrate.The third-order optical nonlinearities of the films were measured by Z-scan technique.The third-order nonlinear susceptibilities（χ^（（3））） of the as-prepared films are 5.9×10^（-7） to 4.29×10^（-6）esu.The surface morphology and composition of the films were characterized by SEM/EDX,which identified that Te metallic particles well dispersed in TeO_x-SiO_2 gel films.展开更多
A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth m...A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.展开更多
A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are ...A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgun's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods.展开更多
The paper proposes a topology optimization method for 1D phononic structures to minimize the tangential component of particle velocity at the objective boundary.The tangential derivative of the boundary integral equat...The paper proposes a topology optimization method for 1D phononic structures to minimize the tangential component of particle velocity at the objective boundary.The tangential derivative of the boundary integral equation(TDBIE)is employed for the evaluation of the objective function involves the tangential derivative quantities.The topological derivative is derived through the adjoint method and the Neumann boundary condition of the adjoint field is obtained using the TDBIE.The average topological derivative which is obtained by calculating the average value of the topological derivative in each layer of design domains,is employed for the updating of the level set function.Numerical implementations demonstrate the proposed method is effective for the design of the 1D phononic crystals with the objective function involving tangential derivative quantities.展开更多
This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This...This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.展开更多
In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators...In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.展开更多
In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time g...In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods.Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes.Numerical examples for two-dimensional problems further confirmthe robustness of the schemes with first-and second-order accurate in time.展开更多
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We the...In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.展开更多
a-Oxo ketene dithioacetals 2 via 1,2-nucleophilie addition by methallyl magnesius chloride afforded corresponding alcohols (3). Treated with water or methanol and catalyzed by Lewis acid, the alcohols 3 were converted...a-Oxo ketene dithioacetals 2 via 1,2-nucleophilie addition by methallyl magnesius chloride afforded corresponding alcohols (3). Treated with water or methanol and catalyzed by Lewis acid, the alcohols 3 were converted regiospecifical ly to substituted phenols 5' or related phenol methyl ethers 5 respectively. This reaction is a novel approach to the synthesis of phenols and their derivatives starting from non-aromatic precursors.展开更多
This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discon...This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discontinuous Galerkin method (LDG) in space. Stability and convergence are demonstrated by a specific choice of numerical fluxes. Finally, the efficiency and accuracy of the scheme are verified by numerical experiments.展开更多
This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We der...This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .展开更多
A new general optimal principle of designing explicit finite difference method was obtained. Several applied cases were put forward to explain the uses of the principle. The validity of the principal was tested by a n...A new general optimal principle of designing explicit finite difference method was obtained. Several applied cases were put forward to explain the uses of the principle. The validity of the principal was tested by a numeric example.展开更多
This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discr...This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discrete vari-ables at the false mesh points are firstly eliminated from the difference schemes andthe local truncation errors are then analyzed in detail.The stability and convergenceof the schemes are proved by energy method.An improvement is proposed to obtainbetter schemes over the original ones.Several numerical examples and comparisonswith other schemes are presented.展开更多
This paper investigates some known difference schemes for the numerical solution to parabolic differential equation with derivative boundary conditions by the fictitious domain method.The stability and convergence in...This paper investigates some known difference schemes for the numerical solution to parabolic differential equation with derivative boundary conditions by the fictitious domain method.The stability and convergence in L ∞ are proven.展开更多
The state of Tb3+ is investigated in liposome. When the concentration of PC is below CMC (critical micell concentration), most of Tb3+ is associated with PC, the binding constant is about 3.35×103 L/mol. When the...The state of Tb3+ is investigated in liposome. When the concentration of PC is below CMC (critical micell concentration), most of Tb3+ is associated with PC, the binding constant is about 3.35×103 L/mol. When the concentration of PC is beyond CMC, most of Tb3+ is dimerized, the dimerization constant is about 3.92×104L/mol. In PC?CH?H2O system, the binding constant of Tb3+?CH complex 2.93×104L/mol is obtained.展开更多
基金extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/174/46.
文摘In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.
基金funded by the Research,Development,and Innovation Authority(RDIA)-Kingdom of Saudi Arabia-with grant number 12803-baha-2023-BU-R-3-1-EI.
文摘This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.
基金Supported by the National Natural Science Foundation of China(11901111)Guangzhou Science and Technology Plan Project(202201011602)。
文摘In this paper,the density-independent fractional diffusion-reaction(FDR)equation involving quadratic nonlinearity is investigated.The fractional derivative is illustrated in the beta derivative sense.We firstly propose Bernoulli(G'/G)-expansion method to study nonlinear fractional differential equations(NFDEs).Subsequently,closed form solutions of the density-independent FDR equation are acquired successfully.In order to better understand the dynamic behaviors of these solutions,3D,contour map and line plots are given by the computer simulation.The results show that the proposed method is a reliable and efficient approach.
基金National Natural Science Foundation of China (60277002)
文摘Two novel poly[(3-alkylthiophene-2,5-diyl)-(benzylidenequinomethane-2,5-diyl)s] derivatives, poly[ (3-butylthiophene-2,5-diyl)-( p-N,N-dimethylamino) benzylidenequinomethane-2,5-diyl) ] ( PBTDMABQ) and poly [( 3-octylthiophene2,5-diyl) -(p-N, N-dimethylamino ) benzylidenequinomethane-2, 5-diyl)] (POTDMABQ), were synthesized.The band gaps of the two polymers are calculated as 1. 75 eV for PBTDMABQ and 1. 69 eV for POTDMABQ,respectively. The homogenous films of the two polymers were prepared and their third-ordernonlinear optical properties were studied by the backward degenerate four-wave mixing at 532 nm. Byusing the relative measurement technique, the third-order nonlinear optical susceptibilities ofPBTDMABQ and POTDMABQ are calculated as 5. 62 X 10^(-9) and 1. 22 X 10^(-8) ESU, respectively. It isfound that substituted alky groups have strong effects on the band gap and nonlinear opticalproperties of the two polymers. The relatively big third-order nonlinear optical susceptibilitiesand small band gap of POTDMABQ resulted mainly from the longer alkyl with strong electron-donatingability can enhance the delocation degree of conjugated π electronics.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
基金supported by Academic Program of Natural Science Foundation Project of CQ CSTC(No 2008BC4003)the Foundation of State Key Laboratory of Physical Chemistry of Solid Surfaces of Xiamen University(No2007)
文摘TeOx-SiO2 composite films having third-order nonlinearities were prepared by electrochemically induced sol-gel deposition method on ITO substrate.The third-order optical nonlinearities of the films were measured by Z-scan technique.The third-order nonlinear susceptibilities（χ^（（3））） of the as-prepared films are 5.9×10^（-7） to 4.29×10^（-6）esu.The surface morphology and composition of the films were characterized by SEM/EDX,which identified that Te metallic particles well dispersed in TeO_x-SiO_2 gel films.
基金National Natural Science Foundation under Grant No. 51179093National Basic Research Program of China under Grant No. 2011CB013602Program for New Century Excellent Talents in University under Grant No.NCET-10-0531
文摘A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.
基金The project supported by the National Natural Science Foundation of China
文摘A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgun's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods.
基金supported by the Fundamental Research Program of Shanxi Province(Grant No.202203021221053)the Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering(Grant No.2022SX-TD021)+3 种基金the National Natural Science Foundation of China(Grant Nos.52075361,and 52274222)the Lvliang Science and Technology Guidance Special Key R&D Project(Grant No.2022XDHZ08)the Major Science and Technology Project of Shanxi Province(Grant No.20201102003)the Key Research and Development Projects in Shanxi province(Grant No.201903D421030).
文摘The paper proposes a topology optimization method for 1D phononic structures to minimize the tangential component of particle velocity at the objective boundary.The tangential derivative of the boundary integral equation(TDBIE)is employed for the evaluation of the objective function involves the tangential derivative quantities.The topological derivative is derived through the adjoint method and the Neumann boundary condition of the adjoint field is obtained using the TDBIE.The average topological derivative which is obtained by calculating the average value of the topological derivative in each layer of design domains,is employed for the updating of the level set function.Numerical implementations demonstrate the proposed method is effective for the design of the 1D phononic crystals with the objective function involving tangential derivative quantities.
文摘This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.
文摘In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.
基金The work is supported by the Guangxi Natural Science Foundation[Grant Numbers 2018GXNSFBA281020,2018GXNSFAA138121]the Doctoral Starting up Foundation of Guilin University of Technology[Grant Number GLUTQD2016044].
文摘In this paper,we consider the numerical schemes for a timefractionalOldroyd-B fluidmodel involving the Caputo derivative.We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods.Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes.Numerical examples for two-dimensional problems further confirmthe robustness of the schemes with first-and second-order accurate in time.
基金The project supported by the China NKBRSF(2001CB409604)
文摘In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.
文摘a-Oxo ketene dithioacetals 2 via 1,2-nucleophilie addition by methallyl magnesius chloride afforded corresponding alcohols (3). Treated with water or methanol and catalyzed by Lewis acid, the alcohols 3 were converted regiospecifical ly to substituted phenols 5' or related phenol methyl ethers 5 respectively. This reaction is a novel approach to the synthesis of phenols and their derivatives starting from non-aromatic precursors.
文摘This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discontinuous Galerkin method (LDG) in space. Stability and convergence are demonstrated by a specific choice of numerical fluxes. Finally, the efficiency and accuracy of the scheme are verified by numerical experiments.
文摘This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .
文摘A new general optimal principle of designing explicit finite difference method was obtained. Several applied cases were put forward to explain the uses of the principle. The validity of the principal was tested by a numeric example.
文摘This paper investigates the stability and convergence of some knowndifference schemes for the numerical solution to heat conduction equation withderivative boundary conditions by the fictitious domain method.The discrete vari-ables at the false mesh points are firstly eliminated from the difference schemes andthe local truncation errors are then analyzed in detail.The stability and convergenceof the schemes are proved by energy method.An improvement is proposed to obtainbetter schemes over the original ones.Several numerical examples and comparisonswith other schemes are presented.
文摘This paper investigates some known difference schemes for the numerical solution to parabolic differential equation with derivative boundary conditions by the fictitious domain method.The stability and convergence in L ∞ are proven.
文摘The state of Tb3+ is investigated in liposome. When the concentration of PC is below CMC (critical micell concentration), most of Tb3+ is associated with PC, the binding constant is about 3.35×103 L/mol. When the concentration of PC is beyond CMC, most of Tb3+ is dimerized, the dimerization constant is about 3.92×104L/mol. In PC?CH?H2O system, the binding constant of Tb3+?CH complex 2.93×104L/mol is obtained.
