Combining Cubic B-Spline Galerkin Method with Quadratic Weight Function for Solving Partial Integro-Differential Equations

Abstract

In this article, a numerical scheme was implemented for solving the partial integro-differential equations (PIDEs) with weakly singular kernel by using the cubic B-spline Galerkin method with quadratic B-spline as a weight function. backward Euler scheme was used for time direction and the cubic B-spline Galerkin method with quadratic weight function was used for spatial derivative. We observed from the numerical examples that the proposed method possesses a high degree of efficiency and accuracy. In addition, the numerical results are in suitable agreement with the exact solutions via calculating L_2 and〖 L〗_∞ norms errors. Theoretically, we discussed the stable evaluation of the current method using the Von-Neumann method, which explained that the present technique is unconditionally stable.