A second order finite difference scheme for singularly perturbed Volterra integro-differential equation

Abstract

In this paper, a singularly perturbed Volterra integro-differential equation, characterised by a single layer, is investigated. A numerical technique which uses a non-standard finite difference scheme is implemented to solve the differential part, furthermore the composite Simpson’s rule on a uniform mesh for the integral part is proposed. Some properties of the discrete problem are discussed and then used to analyse the numerical scheme for convergence. Using Richardson extrapolation, the order of convergence is increased. Numerical simulations are performed to show the applicability of the scheme.

Keywords

• 35K20
• 65M06
• 65M12
• 65M15
• 93C70