A Computational Modeling Based on Trigonometric Cubic B-Spline Functions for the Approximate Solution of a Second Order Partial Integro-Differential Equation

In this paper, the trigonometric cubic B-spline collocation method is extended for the solution of a second order partial integro-differential equations with a weakly singular kernel. The method is obtained by discretization of time derivative using backward finite difference formula while trigonometric cubic B-spline functions are used to approximate the spatial derivative. The scheme is validated through two benchmark test problems. Accuracy of the present approach is assessed in terms of \( L_{\infty } \), \( L_{2} \) error norms and pointwise error. Better accuracy is obtained and the results are compared with quasi wavelet method (QWM), quintic B-spline collocation method (QBCM) and sinc-collocation method using Linsolve Package (SMLP).