Finite Difference Implicit Schemes to Coupled Two-Dimension Reaction Diffusion System - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.4, April 2018

Journal of Applied Mathematics and Physics

Volume 6, Issue 4 (April 2018)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

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

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Download as PDF (Size: 2286KB) PP. 737-753

DOI: 10.4236/jamp.2018.64066 889 Downloads 2,404 Views Citations

Author(s)

Shahid Hasnain¹, Muhammad Saqib², Nawaf Al-Harbi¹

Affiliation(s)

¹Department of Mathematics, Numerical Analysis Division, King Abdulaziz University, Jeddah, KSA.
²Department of Mathematics, Air University, Islamabad, Pakistan.

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.

KEYWORDS

Crank Nicolson, Taylor’s Series, Richardson Extrapolation and Alternating Direction Implicit

Share and Cite:

Hasnain, S. , Saqib, M. and Al-Harbi, N. (2018) Finite Difference Implicit Schemes to Coupled Two-Dimension Reaction Diffusion System. Journal of Applied Mathematics and Physics, 6, 737-753. doi: 10.4236/jamp.2018.64066.

Cited by

[1]	Explicit Finite Difference Analysis of Pseudo-Hyperbolic Partial Differential Equations
	2022

[2]	Wound Healing Modeling Using Partial Differential Equation and Deep Learning
	arXiv preprint arXiv:2111.15632, 2021

[3]	Formulação Híbrida de Elementos Finitos de Alta Ordem para a Resolução de Problemas de Reação-Difusão
	2019

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