Combining cubic B-spline Galerkin method with quadratic weight function for solving partial integro-differential equations

الملخص EN

In this article, a numerical scheme was implemented for solving the partial integrodifferential 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 L2 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.