Trigonometrically-Fitted Simpson’s Method for Solving Volterra Integro-Differential Equations

Abstract

In this study, a third derivative trigonometrically fitted Simpson’s method is developed and applied to approximate the solution of Volterra Integro-Differential Equations (VIDEs) via the multistep collocation method. The VIDEs are first transformed to IVPs by the Leibnitz rule of differentiating integral. A continuous third derivative trigonometrically fitted method is constructed with the trigonometric basis function from which both the main and the complementary discrete formulas are generated. The two discrete formulas are then applied as simultaneous integrators in a block by block form to solve the VIDEs. Whereas numerical properties of the proposed method are investigated, its accuracy is demonstrated through some standard examples.