Retrieval of Timewise Coefficients in the Heat Equation from Nonlocal Overdetermination Conditions

Farah Anwer; M. S. Hussein

doi:10.24996/ijs.2022.63.3.24

Authors

Farah Anwer 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.2022.63.3.24

Keywords:

Neumann boundary problem, inverse problem, coefficient identification problem, nonlinear optimization, heat equation

Abstract

This paper investigates the simultaneous recovery for two time-dependent coefficients for heat equation under Neumann boundary condition. This problem is considered under extra conditions of nonlocal type. The main issue with this problem is the solution unstable to small contamination of noise in the input data. The Crank-Nicolson finite difference method is utilized to solve the direct problem whilst the inverse problem is viewed as nonlinear optimization problem. The later problem is solved numerically using optimization toolbox from MATLAB. We found that the numerical results are accurate and stable.