TITLE:
Solving Stiff Reaction-Diffusion Equations Using Exponential Time Differences Methods
AUTHORS:
H. A. Ashi
KEYWORDS:
Finite Difference Methods, Exponential Integrator, Exponential Time Differencing Method, Reaction-Diffusion System
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.8 No.1,
March
16,
2018
ABSTRACT: Reaction-diffusion equations modeling Predator-Prey
interaction are of current interest. Standard approaches such as first-order
(in time) finite difference schemes for approximating the solution are widely
spread. Though, this paper shows that recent advance methods can be more
favored. In this work, we have incorporated, throughout numerical comparison
experiments, spectral methods, for the space discretization, in conjunction
with second and fourth-order time integrating methods for approximating the
solution of the reaction-diffusion differential equations. The results have
revealed that these methods have advantages over the conventional methods, some of which to mention are: the ease of
implementation, accuracy and CPU time.