University of Hertfordshire

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

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A Laplace Transform Finite Difference Scheme for the Fisher-KPP Equation. / Kane, Stephen; Defreitas, Colin.

In: Journal of Algorithms and Computational Technology, Vol. 15, 28.03.2021.

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@article{84912694bda245b7bbd41d26bbc2a042,
title = "A Laplace Transform Finite Difference Scheme for the Fisher-KPP Equation.",
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.",
keywords = "Fisher-KPP equation, Laplace transform, Stehfest inversion, Talbot inversion, finite difference schemes, travelling wave solutions",
author = "Stephen Kane and Colin Defreitas",
note = "{\textcopyright} The Author(s) 2021. This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/) ",
year = "2021",
month = mar,
day = "28",
doi = "10.1177/1748302621999582",
language = "English",
volume = "15",
journal = "Journal of Algorithms and Computational Technology",
issn = "1748-3018",
publisher = "SAGE Publications Inc.",

}

RIS

TY - JOUR

T1 - A Laplace Transform Finite Difference Scheme for the Fisher-KPP Equation.

AU - Kane, Stephen

AU - Defreitas, Colin

N1 - © The Author(s) 2021. This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/)

PY - 2021/3/28

Y1 - 2021/3/28

N2 - 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.

AB - 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.

KW - Fisher-KPP equation

KW - Laplace transform

KW - Stehfest inversion

KW - Talbot inversion

KW - finite difference schemes

KW - travelling wave solutions

UR - http://www.scopus.com/inward/record.url?scp=85103360827&partnerID=8YFLogxK

U2 - 10.1177/1748302621999582

DO - 10.1177/1748302621999582

M3 - Article

VL - 15

JO - Journal of Algorithms and Computational Technology

JF - Journal of Algorithms and Computational Technology

SN - 1748-3018

ER -