Cubic B-splines collocation method for a class of partial integro-differential equation

In this paper, a numerical method is proposed to estimate the solution of initial-boundary value problems for a class of partial integro-differential equations. This is based on the cubic B-splines method for spatial derivatives while the backward Euler method is used to discretize the temporal derivatives. Detailed discrete schemes are investigated. Next, we proved the convergence and the stability of the proposed method. The method is applied to some test examples and the numerical results have been compared with the exact solutions. The obtained results show the computational efficiency of the method. It can be concluded that computational efficiency of the method is effective for the initial-boundary value problems.