Identification of the unknown heat source terms in a 2D parabolic equation

Abstract

The objective of this paper is to reconstruct the unknown time-dependent heat source terms numerically, for the first time, in a two-dimensional parabolic equation in the rectangular domain with initial and Neumann boundary conditions supplemented by the temperature data as over-determination conditions. Although, the problem is ill-posed (in the sense of Hadamard) but has a unique solution. We apply the forward time central space finite difference scheme along with the Tikhonov regularization to find a stable and accurate numerical solution. The MATLAB subroutine lsqnonlin is used to solve the resulting nonlinear minimization problem. The obtained results show that accurate and stable solutions are achieved. Computational efficiency of the method is investigated by small values of CPU-time.

Keywords

• Inverse source problem
• 2D parabolic equation
• Tikhonov regularization
• Nonlinear optimization