Lie Group Analysis and Wavelet Analysis Method for Solution of a Stefan Problem

Abstract

This paper deals with the solution of a one-phase Stefan melting problem that models the movement of the shoreline in a sedimentary ocean basin which is considered as a moving boundary problem with variable latent heat. The governing partial differential equations are transformed into a set of ordinary differential equations using similarity transformations via the Lie group analysis. We then propose Chebyshev wavelet analysis method for solving the resulting system. A comparison between the solutions obtained by the proposed method and those reported in the literature as well as the exact solution is made to confirm the accuracy and efficiency of the current method.