TITLE:
Finite Difference Implicit Schemes to Coupled Two-Dimension Reaction Diffusion System
AUTHORS:
Shahid Hasnain, Muhammad Saqib, Nawaf Al-Harbi
KEYWORDS:
Crank Nicolson, Taylor’s Series, Richardson Extrapolation and Alternating Direction Implicit
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.4,
April
20,
2018
ABSTRACT: 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.