A fourth Order Pseudoparabolic Inverse Problem to Identify the Time Dependent Potential Term from Extra Condition

M. S.  Hussein; Sayl  Gani

doi:10.24996/ijs.2024.65.8.33

Authors

M. S. Hussein Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-9456-4303
Sayl Gani Department of Mathematics, College of Education for Pure Sciences Ibn-AL-Haithem, University of Baghdad, Baghdad, Iraq / Department of Computer Techniques Engineering, Imam Al-Kadhum College, Baghdad, Iraq https://orcid.org/0000-0003-4595-2251

DOI:

https://doi.org/10.24996/ijs.2024.65.8.33

Keywords:

Von Neumann stability analysis, Finite difference method, Tikhonov regularization method, Pseudoparabolic inverse problem, Inverse problem

Abstract

In this work, the pseudoparabolic problem of the fourth order is investigated to identify the time -dependent potential term under periodic conditions, namely, the integral condition and overdetermination condition. The existence and uniqueness of the solution to the inverse problem are provided. The proposed method involves discretizing the pseudoparabolic equation by using a finite difference scheme, and an iterative optimization algorithm to resolve the inverse problem which views as a nonlinear least-square minimization. The optimization algorithm aims to minimize the difference between the numerical computing solution and the measured data. Tikhonov’s regularization method is also applied to gain stable results. Two examples are introduced to explain the reliability of the proposed scheme. Finally, the results showed that the time dependent potential terms are successfully reconstructed, stable and accurate, even in inclusion of noise.