Beylkin, G., Keiser, J.M. and Vozovoi, L. (1998) A New Class of Time Discretization Schemes for the Solution of Nonlinear PDEs. Journal of Computational Physics, 147, 362-387.
https://doi.org/10.1006/jcph.1998.6093

has been cited by the following article:

• 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.