An effective Legendre wavelet technique for the time-fractional Fisher equation

Document Type : Research Paper

Authors

1 Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey.

2 Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey.

3 1. Department of Mathematics, Izmir Institute of Technology, Izmir, Turkey.\\ 2. Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan.

4 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

Abstract

This study modifies the time-fractional Fisher equation by adding a source term and generalizing the non-linear power to an arbitrary order. A numerical technique is proposed for the modified time-fractional Fisher equation using Legendre wavelets and the quasilinearization technique. The non-linear term is iteratively linearized using the quasilinearization technique. The convergence analysis and error estimates of the proposed method are studied. Several test problems are solved using the proposed technique, and numerical outcomes are contrasted with those obtained using some other approaches existing in the literature.

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Main Subjects

Computational Methods for Differential Equations
Volume 14, Issue 1
January 2026
Pages 145-164

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History

  • Receive Date: 27 September 2024
  • Revise Date: 18 January 2025
  • Accept Date: 27 January 2025

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