Discretization of the Caputo time-fractional advection-diffusion problems with certain wavelet basis function

Authors

  • D. C. Iweobodo
    Department of Mathematics, Dennis Osadebay University, Asaba, Delta State, Nigeria
  • G. C. Abanum
    Department of Mathematics, Dennis Osadebay University, Asaba, Delta State, Nigeria
  • O. Ogoegbulem
    Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria
  • N. I. Ochonogor
    Department of Mathematics, Dennis Osadebay University, Asaba, Delta State, Nigeria
  • I. N. Njoseh
    Department of Mathematics, Delta State University, Abraka, Delta State, Nigeria

Keywords:

Caputo fractional derivatives, Time-fractional advection-diffusion equations (TFADE), Iweobodo-Mamadu-Njoseh wavelet (IMNW), Time discretization, Space discretization

Abstract

Considering the new wavelet-based Galerkin finite element technique constructed with Iweobodo-Mamadu-Njoseh wavelet (IMNW) as the basis function in seeking the numerical solution of time-fractional advection-diffusion equations (TFADE), the TFADE must be simplified to enhance an application of a numerical technique. Thus in this research work, we considered an implementation of the time and space discretization of the TFADE with the
use of IMNW basis function. In order to successfully achieve our result, our methodology inculcated the Caputo fractional derivatives, time fractional advection-diffusion equations (TFADE), Wavelet, IMNW, and Galerkin finite element method. After a successful implementation of the time discretization, an implicit form of TFADE was obtained, followed by the implementation of the space discretization which generated the variational formulation of the equation for easy implementation of the scheme. The illustrated numerical solution from using the new technique provided a resulting numerical evidence which aligns with the exact solution.

Dimensions

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Published

2025-08-01

How to Cite

Discretization of the Caputo time-fractional advection-diffusion problems with certain wavelet basis function. (2025). Journal of the Nigerian Society of Physical Sciences, 7(3), 2405. https://doi.org/10.46481/jnsps.2025.2405

Issue

Volume 7, Issue 3, August 2025

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2025 D. C. Iweobodo, G. C. Abanum, O. Ogoegbulem , N. I. Ochonogor, I. N. Njoseh

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Discretization of the Caputo time-fractional advection-diffusion problems with certain wavelet basis function. (2025). Journal of the Nigerian Society of Physical Sciences, 7(3), 2405. https://doi.org/10.46481/jnsps.2025.2405

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