Determination of Timewise-Source Coefficient in Time-Fractional Reaction-Diffusion Equation from First Order Heat Moment

Authors

  • Qutaiba W. Ibraheem Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • M.S. Hussein Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-9456-4303

DOI:

https://doi.org/10.24996/ijs.2024.65.3.35

Keywords:

Implicit finite difference scheme (IFDS), Tikhonov technique, Caputo fractional derivative, Time-fractional source inverse problem, Stability analysis

Abstract

     This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applied to obtain stable and accurate results. Finally, to demonstrate the accuracy and effectiveness of our scheme, two benchmark test problems have been considered, and its good working with different noise levels.

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Published

2024-03-29

Issue

Section

Mathematics

How to Cite

Determination of Timewise-Source Coefficient in Time-Fractional Reaction-Diffusion Equation from First Order Heat Moment. (2024). Iraqi Journal of Science, 65(3), 1612-1628. https://doi.org/10.24996/ijs.2024.65.3.35

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