A Stable Wavelet Computational Method for the Study of Generalized Burger–Fisher and Burgers–Huxley Models

Khan A., Ghafoor A., Shah K., Abdeljawad T., Alqudah M. A.

Journal of Computational and Theoretical Transport, vol.54, no.6-7, pp.436-461, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 6-7
  • Publication Date: 2025
  • Doi Number: 10.1080/23324309.2025.2580614
  • Journal Name: Journal of Computational and Theoretical Transport
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet
  • Page Numbers: pp.436-461
  • Keywords: Haar wavelet, nonlinear equations, RK-4 solver, stability analysis
  • Istanbul Gelisim University Affiliated: No

Abstract

This work proposes, a hybrid numerical scheme to study the generalized Burger–Fisher equation (gBFE) and generalized Burgers-Huxley equation (gBHE). This strategy comprises Haar wavelet and Runge-Kutta (RK-4) routine solver. We use the collocation approach to approximate the unknown solution and derivatives at discrete points, reducing the given problem to its corresponding nonlinear initial value problem. Then, an efficient time integration scheme is used to solve the consequent system. The proposed technique is implemented for the numerical simulations of various problems that includes gBFE and gBHE. To further elaborate the efficiency of the scheme, (Formula presented.) (Formula presented.) and (Formula presented.) error measures are computed. The computed results are also compared with some existing results in literature. It is observed that the proposed scheme is quite good for the numerical solutions of the gbFE and gBHE model equations. Besides this, the computational stability of the proposed method is examined via the eigenvalues procedure.