1.

Computational analysis of the roles of biochemical reactions in anomalous diffusion dynamics





《中国物理 B》,2016年第4期


Most biochemical processes in cells are usually modeled by reaction–diffusion(RD) equations. In these RD models,the diffusive process is assumed to be Gaussian. However, a growing number of studies have noted that intracellular diffusion is anomalous at some or all times, which may result from a crowded environment and chemical kinetics. This work aims to computationally study the effects of chemical reactions on the diffusive dynamics of RD systems by using both stochastic and deterministic algorithms. Numerical method to estimate the meansquare displacement(MSD) from a deterministic algorithm is also investigated. Our computational results show that anomalous diffusion can be solely due to chemical reactions. The chemical reactions alone can cause anomalous subdiffusion in the RD system at some or all times.The timedependent anomalous diffusion exponent is found to depend on many parameters, including chemical reaction rates, reaction orders, and chemical concentrations.

2.

对流扩散方程修正的交替分组四点方法





王文洽《高等学校计算数学学报》,2005年第27卷第1期


A modified alternating group methods of four points for solving the convectiondiffusion equation is presented here. The method is not only unconditionally stable but also has the advantages of parallel computing. Numerical experiments show that the method is of high accuracy.

3.

Sample Duplication Method for Monte Carlo Simulation of Large ReactionDiffusion System





张红东 陆建明 杨玉良《中国科学B辑(英文版)》,1994年第4期


The sample duplication method for the Monte Carlo simulation of large reactiondiffusion system is proposed in this paper. It is proved that the sample duplication method will effectively raise the efficiency and statistical precision of the simulation without changing the kinetic behaviour of the reactiondiffusion system and the critical condition for the bifurcation of the steadystates. The method has been applied to the simulation of spatial and time dissipative structure of Brusselator under the Dirichlet boundary condition. The results presented in this paper definitely show that the sample duplication method provides a very efficient way to sol'e the master equation of large reactiondiffusion system. For the case of twodimensional system, it is found that the computation time is reduced at least by a factor of two orders of magnitude compared to the algorithm reported in literature.

4.

Streamline upwind finite element method using 6node triangular element with adaptive remeshing technique for convectivediffusion problems





Niphon Wansophark Pramote Dechaumphai《应用数学和力学(英文版)》,2008年第29卷第11期


A streamline upwind finite element method using 6node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convectivediffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.

5.

四阶杆振动方程的两类高精度辛格式





曾文平《高等学校计算数学学报》,2004年第26卷第4期


In this paper, we present two classes of symplectic schemes with high order accuracy for solving fourorder rod vibration equation utt uxxxx=0 via the third type generating function method. First, the equation of four order rod vibration is written into the canonical Hamilton system; second, overcoming successfully the essential difficult on the calculus of high order variations derivative, we get the semidiscretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating function method. Furthermore the discretization of the related modified equation of original equation is obtained. Finally, arbitrary order accuracy symplectic schemes are obtained. Numerical results are also presented to show the effectiveness of the scheme, high order accuracy and properties of excellent longtime numerical behavior.

6.

An improved calculation method for fiber Raman amplifier equations with multiwavelength pumping 被引次数：2





常建华 张明德 孙小菡《中国光学快报(英文版)》,2004年第8期


A novel numerical method for fiber Raman amplifier (FRA) from standard propagation equations is presented and derived based on the onestep method for ordinary differential equation (ODE). The proposed algorithm is effective in solving FRA equations including all the interactions among pumps, signals, and noises. Applications of the numerical analysis to practical FRAbased systems show a great reduction in computation time in comparison with the average power method and the fourthorder RungeKutta (RK) method, under the same condition. Also the proposed method can decrease the computing time over three orders of magnitude with excellent accuracy promises in comparison with the direct integration method.

7.

New complex variable meshless method for advectiondiffusion problems





王健菲 程玉民《中国物理 B》,2013年第3期


In this paper,an improved complex variable meshless method(ICVMM) for twodimensional advectiondiffusion problems is developed based on improved complex variable moving leastsquare(ICVMLS) approximation.The equivalent functional of twodimensional advectiondiffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advectiondiffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advectiondiffusion problems,and has a good convergent character,accuracy,and computational efficiency.

8.

Analysis of variable coefficient advectiondiffusion problems via complex variable reproducing kernel particle method





翁云杰 程玉民《中国物理 B》,2013年第9期


The complex variable reproducing kernel particle method （CVRKPM） of solving twodimensional variable coefficient advectiondiffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a twodimensional problem is formed with a onedimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for twodimensional variable coefficient advectiondiffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method （RKPM） and the element free Galerkin （EFG） method.

9.

A new simplified ordered upwind method for calculating quasipotential





虞晴 刘先斌《中国物理 B》,2022年第1期


We present a new method for calculation of quasipotential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the firstorder line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasipotential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP.

10.

Alternating Direction Finite Volume Element Methods for ThreeDimensional Parabolic Equations





Tongke《高等学校计算数学学报(英文版)》,2010年第3卷第4期


This paper presents alternating direction finite volume element methods for threedimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with secondorder splitting error, the other two schemes have thirdorder splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 seminorm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

11.

线性定常对流占优对流扩散问题的有限体积——流线扩散有限元法





张文博 孙澈《计算数学》,2004年第26卷第1期


In this paper, two kinds of Finite VolumeStreamline Diffusion Finite Element methods (FVSD) for steady convection dominateddiffusion problem are presented and the stability and error estimation for the numerical schemes considered are established in the norm stronger than L^2norm. The theocratical analysis and numerical example show that the schemes constructed in this paper are keeping the basic properties of Streamline Diffusion (SD) method and they are more economical in computing scale than SD scheme, and also, they have same accuracy as FVGalerkin FE method and better stability than it.

12.

MHD flow and mass transfer of chemically reactive upper convected Maxwell fluid past porous surface





吴朝安《应用数学和力学(英文版)》,2012年第33卷第7期


The magnetohydrodynamic (MHD) flow and mass transfer of an electrically conducting upper convected Maxwell (UCM) fluid at a porous surface are studied in the presence of a chemically reactive species. The governing nonlinear partial differential equations along with the appropriate boundary conditions are transformed into nonlinear ordinary differential equations and numerically solved by the Kellerbox method. The effects of various physical parameters on the flow and mass transfer characteristics are graphically presented and discussed. It is observed that the order of the chemical reaction is to increase the thickness of the diffusion boundary layer. Also, the mass transfer rate strongly depends on the Schmidt number and the reaction rate parameter. Furthermore, available results in the literature are obtained as a special case.

13.

HIGHORDER BOUNDARY CONDITIONS FOR THE PROBLEMS OF LAPLACE EQUATION IN INFINITE REGION AND THEIR APPLICATION





黄河宁 王发君《应用数学和力学(英文版)》,1990年第11卷第11期


The highorder boundary conditions for the problems of Laplace equation in infiniteregion have been developed.The improvement in accuracy for numerical solution isachieved by imposing the highorder boundary conditions on the exterior boundary of areduced finite region in which the numerical method is used.So both the computing effortsand the required storage in computer are reduced.The numerical examples show that thelstorder boundary condition approaches to the exact boundary condition and it is clearlysuperior to the traditional boundary condition and the2ndorder boundary condition.

14.

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTIONDIFFUSION EQUATIONS





Yuanming Wang ;Benyu Guo《计算数学(英文版)》,2008年第2期


A monotone compact implicit finite difference scheme with fourthorder accuracy in space and secondorder in time is proposed for solving nonlinear reactiondiffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate of.the iteration.

15.

THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD





钟阳 张永山《应用数学和力学(英文版)》,2006年第27卷第6期


The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution.

16.

Time domain finite volume method for the transient response and natural characteristics of structuralacoustic coupling in an enclosed cavity





XUAN Lingkuan ;MING Pingjian ;ZHANG Wenping ;JIN Guoyong ;GONG Jingfeng《Chinese Journal of Acoustics》,2014年第3期


A time domain finite volume method（TDFVM）based on wave theory is developed to analyze the transient response and natural characteristics of structuralacoustic coupling problems in an enclosed cavity.In the present method,the elastic dynamic equations and acoustic equation in heterogeneous medium are solved in solid domains and fluid domains respectively.The structuralacoustic coupling is implemented according to the continuity condition of the particle velocity along the normal direction and the normal traction equilibrium condition on the interface.Several numerical examples are presented to validate the effectiveness and accuracy of the present TDFVM.Then the effects of water depth on the acoustic and vibration characteristics and the natural characteristics of a structuralacoustic coupling system are analyzed.The numerical results show that the increase of water depth leads to a stronger coupling between the water and structure and the decrease of natural frequencies of coupling system,The computational cost and memory of this method are small and it can be applicable to structuralacoustic coupling problems in the heterogeneous fluid.

17.

UNSTEADY／STEADY NUMERICAL SIMULATION OF THREEDIMENSIONAL INCOMPRESSIBLE NAVIERSTOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY





温功碧 陈作斌《应用数学和力学(英文版)》,2004年第25卷第1期


A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible NavierStokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a thirdorder fluxdifference splitting technique for the convective terms and the secondorder central difference for the viscous terms. The numerical flux of semidiscrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of BaldwinLomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of BaldwinLomax could not exactly predict the flow.

18.

Propagation of Rayleigh waves on free surface of transversely isotropic generalized thermoelastic diffusion





Rajneesh Kumar Tarun Kansal《应用数学和力学(英文版)》,2008年第29卷第11期


The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive halfspace, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The GreenLindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.

19.

Finite Difference Method for ReactionDiffusion Equation with Nonlocal Boundary Conditions 被引次数：2





Jianming Liu 《高等学校计算数学学报(英文版)》,2007年第16卷第2期


In this paper, we present a numerical approach to a class of nonlinear reactiondiffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A secondorder accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2norm. A simple numerical example is given to illustrate the efficiency of the proposed method.

20.

HIGH RESOLUTION SCHEMES FOR CONSERVATION LAWS AND CONVECTIONDIFFUSION EQUATIONS WITH VARYING TIME AND SPACE GRIDS





Huazhong Tang Gerald Warnecke《计算数学(英文版)》,2006年第24卷第2期


This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convectiondiffusion equations, by projecting the solution increments of the underlying partial differential equations （PDE） at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L^∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higherorder spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD RungeKutta scheme or a LaxWendroff type method, respectively. The schemes are used to solve a linear convectiondiffusion equation, the nonlinear inviscid Burgers＇ equation, the one and twodimensional compressible Euler equations, and the twodimensional incompressible NavierStokes equations. The numerical results show that the schemes are of higherorder accuracy, and efficient in saving computational cost, especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained, although the schemes are slightly nonconservative.
