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

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Document pages: 17 pages

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

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