Implicit-explicit time discretization coupled with finite element methods for delayed predator-prey competition reaction-diffusion system

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• 作者：Aiguo Xiao ; ^{xag@xtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Gengen Zhang ; Jie Zhou
• 关键词：Implicit&ndash ; explicit multistep methods ; Finite element method ; Error estimate ; Predator&ndash ; prey system ; Breaking points
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：71
• 期：10
• 页码：2106-2123
• 全文大小：437 K

文摘

The main purpose of this paper is to develop the two-step implicit–explicit(IMEX) time discretization coupled with finite element methods for solving delayed predator–prey competition reaction–diffusion system. Finite element methods are used to discretize the space variables, both IMEX two-step one-leg methods and IMEX linear two-step methods are considered in time discretization, where the nonlinear reaction part is discretized explicitly and the diffusion part is discretized implicitly. The L²$L^2$-norm error estimates with handling the breaking points are derived. These methods only require solving two independent linear systems with the same coefficient matrix at different time, and avoid solving large-scale systems of nonlinear algebraic equations, thus the resulting schemes are efficient. Some numerical experiments are presented to confirm the theoretical results.