Legendre wavelet modified petrov–galerkin method in two-dimensional moving boundary problem

Abstract

In this study, we developed the two-dimensional Legendre wavelet modified Petrov–Galerkin method for solving the two-dimensional moving boundary problem arising during melting of solid whose one surface is kept under most generalised boundary condition, and other two surfaces are insulated. The particular cases when surface subjected to the boundary condition of first, second and third kinds are discussed in detail. For validity of the present method, we have plotted graphs between residual (obtained from the original differential equation and its associated boundary conditions) and x-axis and found the effect of an error on moving layer thickness and y coordinate, respectively. Furthermore, we proved the convergence analysis of present method. The effect of parameters (Predvoditelev number, Kirpichev number, Biot number) on the moving layer thickness is discussed in detail. The whole analysis is presented in a dimensionless form.