Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets

In this paper we reduce a free boundary problem from heat transfer to a weaklysingular volterra integral equation of the first kind. since the first kind integralequation is ill posed, and an appropriate method for such ill posed problems is based onwavelets, then we apply the chebyshev wavelets to solve the integral equation.numerical implementation of the method is illustrated by two benchmark problemsoriginated from heat transfer. the behavior of the initial and free boundary heatfunctions along the position axis during the time have been shown through some threedimensional plots. the convergence of the method is pointed in the end of section 2.the numerical examples show the accuracy and applicability of the method from application and programming points of views.