摘要
This paper is concerned with the stability analysis of the exact and numerical solutions of the reaction-diffusion equations with distributed delays. This kind of partial integro-differential equations contains time memory term and delay parameter in the reaction term. Asymptotic stability and dissipativity of the equations with respect to perturbations of the initial condition are obtained. Moreover, the fully discrete approximation of the equations is given. We prove that the one-leg θ-method preserves stability and dissipativity of the underlying equations. Numerical example verifies the efficiency of the obtained method and the validity of the theoretical results.
This paper is concerned with the stability analysis of the exact and numerical solutions of the reaction-diffusion equations with distributed delays. This kind of partial integro-differential equations contains time memory term and delay parameter in the reaction term. Asymptotic stability and dissipativity of the equations with respect to perturbations of the initial condition are obtained. Moreover, the fully discrete approximation of the equations is given. We prove that the one-leg θ-method preserves stability and dissipativity of the underlying equations. Numerical example verifies the efficiency of the obtained method and the validity of the theoretical results.
基金
The authors thank the referees very much for their very valuable suggestions in improving the paper. This work was supported by the National Natural Science Foundation of China （Grant No. 11271311）, the Research Foundation of Education Commission of Hunan Province of China （14A146）, and the Hunan Province Innovation Foundation for Postgraduate （CX2014B253）.
