Analyzing Similarity Solution of Modified Fisher Equation

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Duruk E. H., Köksal M. E., Jiwari R.

JOURNAL OF MATHEMATICS, vol.2022, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2022
  • Publication Date: 2022
  • Doi Number: 10.1155/2022/6806906
  • Journal Name: JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we first examine the type of structure of the solutions to the modified form of a nonlinear Fisher's reaction-diffusion equation. The existence of the traveling wave solution to the equation in the long term is observed by using dynamical system theory and exhibiting a phase space analysis of its stable points. In parallel, we represent radial basis functions (RBFs)-based differential quadrature methods (DQMs) to close the solution of the equation. The stability analysis of the recommended method is demonstrated. Some initial-boundary value problems are considered test problems. The numerical results indicate extremely exact and stable initial and boundary conditions in the same domain with dissimilar time ranges.