Numerical Approximation of the One-dimensional Inverse Stefan Problem Using a Meshless Method

This paper employs a recent algorithm capable of determining an optimal regularization technique based on a meshless method of fundamental solutions for the onedimensional inverse Stefan problem, where the boundary data is reconstructed on the fixed boundary. The inverse problem is ill-posed. For comparison purposes, we employ Tikhonov, Truncated Singular Value Decomposition, and Randomized Singular Value Decomposition regularization methods to obtain a more accurate solution. The numerical results of three different benchmark examples are presented in this paper.