Shalf, J.S., Sundip, D.S. and John, M.J. (2010) Exascale Computing Technology Challenges. In: Palma, J.M.L.M., Daydé, M., Marques, O. and Lopes, J.C., Eds., High Performance Computing for Computational Science—VECPAR 2010, Lecture Notes in Computer Science, Vol. 6449, Springer, Berlin, Heidelberg, 1-25.

has been cited by the following article:

• 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.