Inverse two-phase nonlinear Stefan and Cauchy-Stefan problems: A phase-wise approach

We develop a novel phase-wise sequential numerical approach based on the method of fundamental solutions (MFS) for inverse two-phase nonlinear Stefan and Cauchy-Stefan problems in one dimension (1D). By treating each phase independently, the inverse two-phase nonlinear Stefan problem splits into two single-phase inverse problems: an inverse nonlinear boundary identification problem and an inverse linear one-phase Stefan problem. Along with the reconstruction of boundary data, the simultaneous reconstruction of the boundary and initial data is also considered. Numerical investigations show the robustness and efficiency of the proposed method in reconstructing the data