Numerical Study of One Dimensional Fishers KPP Equation with Finite Difference Schemes

• 作者: Muhammad Saqib Shahid Hasnain
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: FORWARD in Time and CENTRE in Space (FTCS) LAX Wendroff Taylor’s Series CRANK Nicolson and RICHARDSON EXTRAPOLATION
• 年，卷（期）: 2017,（1）
• 页码范围: 70-83
• 页数: 14页
• 分类号: O1

摘要

In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that our schemes are indeed stable under certain choices of the model and numerical parameters. Numerical comparisons with analytical solution are also discussed. Numerical results show that Crank Nicolson and Richardson extrapolation are very efficient and reliably numerical schemes for solving one dimension fisher’s KPP equation.