Cubic Bsplines collocation method for solving a partial integrodifferential equation with a weakly singular kernel

In this paper, we apply a numerical scheme for the solution of a second order partial integrodifferential equation with a weakly singular kernel. In the time direction, the backward Euler method timestepping is used to approximate the differential term and the cubic Bsplines is applied to the space discretization. Detailed discrete schemes, the convergence and the stability of the method is demonstrated. Next, the computational efficiency and accuracy of the method are examined by the numerical results.