Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results obtained here can be compared with the cubic B-spline method. In addition, solving some examples demonstrates the validity and applicability of the approached method, so that the results are reported in the tables and their figures are shown. The high speed of the calculations and the assurance of having an approximate solution are obtained by proving the stability of the method.