Legendre wavelets technique for special Initial-Value problem for the quarter plain of heat transfer

In this paper we have solved the heat transfer equation by means of the Volterra integral equation and Legendre Wavelets. Since, due to numerical facts, solution of the related partial differential equation is difficult, thus we have applied integral equation model. The integral equation model of this system is a Volterra type of the first kind. These systems are ill posed system, and appropriate method for such systems are wavelets, since wavelets can be generated in the space of solutions. In this work we apply the Legendre wavelets to solve the corresponding integral equation. Numerical implementation of the method is illustrated by benchmark problems originated from heat transfer. The behavior of the initial heat function along with the position axis during the time have been shown through three dimensional plots.