Document Type: Original Paper

**Author**

Department of Mathematics, Faculty of science, Qom University of Technology, Qom, Iran

**Abstract**

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.

**Keywords**

- Volterra integral equation of the first kind
- Heat equation
- Numerical solution
- Second kind Chebyshev wavelets
- Free boundary

**Main Subjects**

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