Numerical solution of heat equation with specification of heat flux on the boundary by the Legendre Wavelets

In this paper I consider an Initial-Boundary-Value problem from heat transfer. The solution of this problem represent in some series forms. Such series have integral terms. Every integral is weakly singular. I approximate the integrals and so the solution, by the Legendre wavelets. The accuracy and efficiency of the method is illustrated by two benchmark examples from heat transfer