Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme

• 作者: Daoud Suleiman Mashat 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) Taylor’s Series CRANK Nicolson ALTERNATING Direction IMPLICIT (ADI) SCHEME
• 年，卷（期）: 2017,（2）
• 页码范围: 183-194
• 页数: 12页
• 分类号: O1

摘要

This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.