FIRST-ORDER AND SECOND-ORDER, CHAOS-FREE, FINITE DIFFERENCE SCHEMES FOR FISHER EQUATION

• 来源期刊: 计算数学(英文版)
• 学科: 数学
• 关键词: Reaction-diffusion equation Fidelity algorithm.
• 年，卷（期）: 2001,（5）
• 页码范围: 519-530
• 页数: 12页
• 分类号: O1
• 语种: 英文

摘要

A new class of finite difference schemes is constructed for Fisher partial differential equation i.e. the reaction-diffusion equation with stiff source term: αu(1 - u). These schemes have the properties that they reduce to high fidelity algorithms in the diffusion free case namely in which the numerical solutions preserve the properties inherent in the exact solutions for arbitrary time step-size and reaction coefficient α ＞ 0, and all non physical spurious solutions including bifurcations and chaos that normally appear in the standard discrete models of Fisher partial differential equation will not occur. The implicit schemes so developed obtain the numerical solutions by solving a single linear algebraic system at each step. The boundness and asymptotic behaviour of numerical solutions obtained by all these schemes are given. The approach constructing the above schemes can be extended to reaction-diffusion equations with other stiff source terms.