摘要
In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order 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 L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.
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 second-order 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 L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.
基金
The work of Liu was supported by National Natural Science Foundation of China （Tian-yuan Foundation） under grant 10626044
Foundation of Research Starmp of Xuzhou Normal University （KY2004111）
The work of Sun was supported by National Natural Science Foundation of China under grant 10471023.
关键词
反应扩散方程
非局部边界条件
有限差分法
可解性
收敛
Reaction-diffusion
nonlocal Robin type boundary
finite difference
solv-ability
convergence.
