Numerical Determination of Thermal Conductivity in Heat Equation under Nonlocal Boundary Conditions and Integral as Over specified Condition

Sara Salim Weli; M. S. Hussein

doi:10.24996/ijs.2022.63.11.31

Authors

Sara Salim Weli 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.2022.63.11.31

Keywords:

heat equation, inverse problem , nonlocal boundary condition , integral overdetermination condition

Abstract

In this article, an inverse problem of finding timewise-dependent thermal conductivity has been investigated numerically. Numerical solution of forward (direct) problem has been solved by finite-difference method (FDM). Whilst, the inverse (indirect) problem solved iteratively using Lsqnonlin routine from MATLAB. Initial guess for unknown coefficient expressed by explicit relation based on nonlocal overdetermination conditions and intial input data .The obtained numrical results are presented and discussed in several figures and tables. These results are accurate and stable even in the presense of noisy data.