摘要
文章给出一类带记忆的非线性反应扩散方程的数值解法,在该类方程中通常的扩散项被一般意义下的卷积所替代。对于非线性项的处理首先对空间上进行梯度运算,冻结非线性项梯度系数进行线性化处理,再采用高精度的六点隐式差分格式进行半离散处理;时间上采用Laplace变换的数值逆方法。理论上分析了该算法的截断误差,数值实验表明了该方法是可行的。
This paper presents a numerical method for the nonlinear reaction-diffusion equation with memory. The usual diffusion term is replaced by a convolution integral. For the nonlinear part, firstly it employs the grade operator, so that it turns out to be the linear equation. Secondly, in the direction of space x,it uses six-point implicit schemes, and in the direction of time t, uses numerical inversion for the Laplace transformation. The truncation error of this algorithm is theoretically analyzed,and a numerical example shows that the presented method is feasible.
出处
《合肥工业大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第2期265-269,共5页
Journal of Hefei University of Technology：Natural Science
关键词
非线性
带记忆
反应扩散方程
数值方法
LAPLACE变换
nonlinearity
memory effect
reaction-diffusion equation
numerical method
Laplace transformation
