Solving Integro-Differential Boundary Value Problems Using Sinc-Derivative Collocation

Abstract

In this paper, the sinc-derivative collocation approach is used to solve second order integro-differential boundary value problems. While the derivative of the unknown variables is interpolated using sinc numerical methods, the desired solution and the integral terms are evaluated through numerical integration and all higher order derivatives are approximated through successive numerical differentiation. Suitable transformations are used to reduce non-homogeneous boundary conditions to homogeneous. Comparison of the proposed method with different approaches that were previously considered in the literature is carried out in order to test its accuracy and efficiency. The results show that the sinc-derivative collocation method performs well.

Keywords

• integro-differential equation
• boundary value problems
• sinc-derivative
• numerical methods
• sinc-collocation