Numerical solution of an Initial-Boundary value Problem by Barycentric-Product integration method on all times

In this paper we consider an initial-boundary value problem from heat conduction. We reduce the heat conduction problem to a two weakly singular Volterra integral equations of the second kind. We describe the barycentric-product integration method on unite interval and extend it to big length intervals by the sense of lag terms. Efficiency and accuracy of the method is illustrated by two sample problem originated from heat conduction.