A Laplace transform finite difference scheme for the Fisher-KPP equation. (March 2021)

• Record Type: Journal Article
• Authors: Defreitas, Colin L; Kane, Steve J
• Is Part Of: Journal of algorithms & computational technology. Volume 15(2021)
• Publication Date: 2021-03
• Subjects: Laplace transform -- Fisher-KPP equation -- travelling wave solutions -- Talbot inversion -- Stehfest inversion -- finite difference schemes; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748302621999582
• Languages: English
• ISSNs: 1748-3018

Abstract

This paper proposes a numerical approach to the solution of the Fisher-KPP reaction-diffusion equation in which the space variable is developed using a purely finite difference scheme and the time development is obtained using a hybrid Laplace Transform Finite Difference Method (LTFDM). The travelling wave solutions usually associated with the Fisher-KPP equation are, in general, not deemed suitable for treatment using Fourier or Laplace transform numerical methods. However, we were able to obtain accurate results when some degree of time discretisation is inbuilt into the process. While this means that the advantage of using the Laplace transform to obtain solutions for any time t is not fully exploited, the method does allow for considerably larger time steps than is otherwise possible for finite-difference methods.