10.57647/j.jtap.2024.1805.62

A numerical solution for a nonlinear inverse stochastic parabolic problem based on Legendre wavelets bases

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  • Samaneh Parvaz1,
  • Ali Zakeri*1,
  1. Faculty of Mathematics, Khajeh Nasir Toosi University of Technology, Tehran, Iran
A numerical solution for a nonlinear inverse stochastic parabolic problem based on Legendre wavelets bases

Received: 2024-08-07

Revised: 2024-08-27

Accepted: 2024-08-31

Published in Issue 2024-10-30

Copyright (c) 2024 Samaneh Parvaz, Ali Zakeri (Author)

Creative Commons License

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

How to Cite

1.
Parvaz S, Zakeri A. A numerical solution for a nonlinear inverse stochastic parabolic problem based on Legendre wavelets bases. J Theor Appl phys. 2024 Oct. 30;18(5):1-8. Available from: https://oiccpress.com/jtap/article/view/8197
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Abstract

In this paper, we consider a 1D nonlinear stochastic partial differential equation of parabolic type.
In this problem, values of the function on a part of physical boundary of the domain are unknown.
A numerical approach has been developed to approximate the exact solution for this issue by
employing Legendre wavelets and their operational matrix. This method is combined with the
Levenberg-Marquardt regularization technique. In continuation, the error analysis is given. Finally,
a numerical sample confirms the efficiency and accuracy of this method.

Keywords

  • Stochastic partial differential equation (SPDE),
  • Legendre wavelets,
  • Levenberg-Marquardt regularization
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