University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 30 4 2019 11 01 Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets 355 362 73610 10.22059/jsciences.2019.279230.1007393 EN Bahman Babayar-Razlighi Department of Mathematics, Faculty of science, Qom University of Technology, Qom, Iran Journal Article 2019 04 27 In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two benchmark problems originated from heat transfer. The behavior of the initial and free boundary heat functions along the position axis during the time have been shown through some three dimensional 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. https://jsciences.ut.ac.ir/article_73610_496879cb1914862cb20e4b9b96966c43.pdf