Author(s)

Shahid Hasnain, Daoud Suleiman Mashat, Muhammad Saqib, Shafeek A. Ghaleb, Noorah Y. Mshary

Department of Mathematics, Numerical Analysis, King Abdulaziz University, Jeddah, Saudi Arabia.

This research paper represents a numerical approximation to non-linear coupled one dimension reaction diffusion system, which includes the existence and uniqueness of the time dependent solution with upper and lower bounds of the solution. Also numerical approximation is obtained by finite difference schemes to reach at reasonable level of accuracy, which is magnified by L₂, L_∞ and relative error norms. The accuracy of the approximations is shown by randomly selected grid points along time level and comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations with a little modifications.

Forward in Time and Centre in Space (FTCS), Taylor’s Series, Crank Nicolson, Fourth Order Implicit Scheme and Richardson Extrapolation

Hasnain, S. , Mashat, D. , Saqib, M. , A. Ghaleb, S. and Y. Mshary, N. (2017) Numerical Approximation to Nonlinear One Dimensional Coupled Reaction Diffusion System. Journal of Applied Mathematics and Physics, 5, 1551-1574. doi: 10.4236/jamp.2017.58129.