A Computational Technique for the Solution of Parabolic Type Integro-Differential Equation with a Weakly Singular Kernel

Abstract

A quartic B-spline collocation method is proposed for numerical solution of partial integro-differential equations with a weakly singular kernel. The scheme is developed by discretization of the time derivative using forward difference formula while the spatial derivative is approximated using quartic B-spline functions. Numerical solution of two test problems are provided to validate the scheme. Accuracy of the method is assessed in terms of ܮ ∞and ܮଶ error norms. Better accuracy is obtained and the results are also compared with cubic B-spline collocation method.