Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method

Abstract

Abstract We provide the numerical solution of a Volterra integro-differential equation of parabolic type with memory term subject to initial boundary value conditions. Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc-collocation method is employed in space. A weakly singular kernel has been viewed as an important case in this study. The convergence analysis has been discussed in detail, which shows that the approach exponentially converges to the solution. Furthermore, numerical examples and illustrations are presented to prove the validity of the suggested method.

Keywords

• partial integro-differential equation
• sinc-collocation method
• finite difference method
• product trapezoidal integration rule