In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co...In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.展开更多
In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experiment...In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experimental data the mathematical model for calculating the concentration of metal at different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for the partial differential equations （PDEs） of the elliptic type of second order with piece-wise diffusion coefficients in the three layer domain. We develop here a finite-difference method for solving a problem of the above type with the periodical boundary condition in x direction. This procedure allows reducing the 3-D problem to a system of 2-D problems by using a circulant matrix.展开更多
The mechanism of transport of chemicals in soil is an important research topic of environmental science and engineering, and some models and methods for a variety of solute transport problems have been done. Howeve...The mechanism of transport of chemicals in soil is an important research topic of environmental science and engineering, and some models and methods for a variety of solute transport problems have been done. However. most of previous works are usually for a soil column of infinite dimension. Starting from the one-dimension transient solute transport equation and its boundary and initial condition for a solute transport problem of soil column of finite length, this work has successfully applied a variable transformation to simplify the partial differential equation of solute transport problem. And an analytical serial solution for the simplified equation is then established by the so-called separated variable method and the superposition method. Compared with numerical methods such as finite different method and finite element method, this analytical solution is more accurate and of higher computation efficiency. In addition, the solution procedure presented could be extended for applications such as quality analysis, design of physical experimentation, or parameter estimation and measurement of solute transport problems.展开更多
A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The s...A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.展开更多
基金the National Key Basic Research Project of China under
文摘In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.
文摘In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experimental data the mathematical model for calculating the concentration of metal at different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for the partial differential equations （PDEs） of the elliptic type of second order with piece-wise diffusion coefficients in the three layer domain. We develop here a finite-difference method for solving a problem of the above type with the periodical boundary condition in x direction. This procedure allows reducing the 3-D problem to a system of 2-D problems by using a circulant matrix.
基金Acknowledgements： The work was supported by the National Natural Science Foundation of China （No. 90502006/D0123）, Hunan provincial Natural Science Foundation of China （No. 06JJ3020） and Scientific Research Fund of Hunan Provincial Education Department （No. 06C500）.
文摘The mechanism of transport of chemicals in soil is an important research topic of environmental science and engineering, and some models and methods for a variety of solute transport problems have been done. However. most of previous works are usually for a soil column of infinite dimension. Starting from the one-dimension transient solute transport equation and its boundary and initial condition for a solute transport problem of soil column of finite length, this work has successfully applied a variable transformation to simplify the partial differential equation of solute transport problem. And an analytical serial solution for the simplified equation is then established by the so-called separated variable method and the superposition method. Compared with numerical methods such as finite different method and finite element method, this analytical solution is more accurate and of higher computation efficiency. In addition, the solution procedure presented could be extended for applications such as quality analysis, design of physical experimentation, or parameter estimation and measurement of solute transport problems.
基金supported by National Center for Mathematics and Interdisciplinary Sciences,CASNational Natural Science Foundation of China (Grant Nos. 60931002 and 91130019)
文摘A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.
