A Laplace Transform Finite Difference Scheme for the Fisher-KPP Equation.

Stephen Kane, Colin Defreitas

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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.
Original languageEnglish
Number of pages11
JournalJournal of Algorithms and Computational Technology
Volume15
Early online date28 Mar 2021
DOIs
Publication statusE-pub ahead of print - 28 Mar 2021

Keywords

  • Fisher-KPP equation
  • Laplace transform
  • Stehfest inversion
  • Talbot inversion
  • finite difference schemes
  • travelling wave solutions

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