Cubic B-spline for the Numerical Solution of Parabolic Integro-differential Equation with a Weakly Singular Kernel

Abstract

The aim of study is to solve parabolic integro-differential equation with a weakly singular kernel. Problems involving partial integro-differential equations arise in fluid dynamics, viscoelasticity, engineering, mathematical biology, financial mathematics and other areas. Many mathematical formulations of physical phenomena contain integro-differential equations. Integro-differential equations are usually difficult to solve analytically so, it is required to obtain an efficient approximate solution. A numerical method is developed to solve the partial integro-differential equation using the cubic B-spline collocation method. The method is based on discretizing the time derivative using finite central difference formula and the cubic B-spline collocation method for the spatial derivative. Three examples are considered to illustrate the efficiency of the method developed. It is to be observed that the numerical results obtained by the proposed method efficiently approximate the exact solutions.