Comparative Study of MFS with Tikhonov and RSVD for the Backward Heat Conduction Problem

Abstract

This paper investigated an application designed to identify the most effective regularization technique by employing a meshless method of fundamental solutions to address the backward heat conduction problem (BHCP), which is characterized by its ill-posed nature. To enable a comparative analysis, this study applies both the Tikhonov and Randomized Singular Value Decomposition regularization methods to improve solution accuracy and stability. The numerical results from two benchmark examples are presented in this paper.