Numerical Solution to Recover Time-dependent Coefficient and Free Boundary from Nonlocal and Stefan Type Overdetermination Conditions in Heat Equation

  • Mohammed Qassim Department of Energy, College of Engineering Al-Musayab, University of Babylon, Babel, Iraq
  • M. S. Hussein Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-9456-4303
Keywords: inverse problem, coefficient identification problem, nonlinear optimization, FDM

Abstract

This paper investigates the recovery for time-dependent coefficient and free boundary for heat equation. They are considered under mass/energy specification and Stefan conditions. The main issue with this problem is that the solution is unstable and sensitive to small contamination of noise in the input data. The Crank-Nicolson finite difference method (FDM) is utilized to solve the direct problem, whilst the inverse problem is viewed as a nonlinear optimization problem. The latter problem is solved numerically using the routine optimization toolbox lsqnonlin from MATLAB. Consequently, the Tikhonov regularization method is used in order to gain stable solutions. The results were compared with their exact solution and tested via root mean squares error (RMSE). We found that the numerical results are accurate and stable.

Published
2021-03-30
How to Cite
Mohammed Qassim, & M. S. Hussein. (2021). Numerical Solution to Recover Time-dependent Coefficient and Free Boundary from Nonlocal and Stefan Type Overdetermination Conditions in Heat Equation. Iraqi Journal of Science, 62(3), 950-960. https://doi.org/10.24996/ijs.2021.62.3.25
Section
Mathematics