One-Dimensional Inverse Stefan Problem Numerical Approximation Utilizing a Meshless Method
摘要
We extend a meshless method of fundamental solutions to the one-dimensional inverse Stefan problem for the heat equation, where the boundary data is to be reconstructed on the fixed boundary. The inverse problem is ill-posed for small errors in the input measured data can cause high deviations in solution. Therefore, we incorporate Tikhonov regularization to obtain a stable solution. Numerical results are presented.