Finite Difference Implicit Schemes to Coupled Two-Dimension Reaction Diffusion System

• 作者: Muhammad Saqib Nawaf Al-Harbi Shahid Hasnain
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: CRANK Nicolson Taylor’s Series RICHARDSON EXTRAPOLATION and ALTERNATING Direction IMPLICIT
• 年，卷（期）: 2018,（4）
• 页码范围: 737-753
• 页数: 17页
• 分类号: O1

摘要

In this research article, two finite difference implicit numerical schemes are described to approximate the numerical solution of the two-dimension modified reaction diffusion Fisher’s system which exists in coupled form. Finite difference implicit schemes show unconditionally stable and second-order accurate nature of computational algorithm also the validation and comparison of analytical solution, are done through the examples having known analytical solution. It is found that the numerical schemes are in excellent agreement with the analytical solution. We found, second-implicit scheme is much faster than the first with good rate of convergence also we used NVIDA devices to accelerate the computations and efficiency of the algorithm. Numerical results show our proposed schemes with use of HPC (High performance computing) are very efficient and reliable.