Numerical Approach for Delay Volterra Integro-Differential Equation

Abstract

The delay integro-differential equation for the Volterra type has been solved by using the two-point multistep block (2PBM) method with constant step-size. The proposed block method of order three is formulated using Taylor expansion and will simultaneously approximate the numerical solution at two points. The 2PBM method is developed by combining the predictor and corrector formulae in the PECE mode. The predictor formulae are explicit, while the corrector formulae are implicit. The algorithm for the approximate solutions were constructed and analyzed using the 2PBM method with Newton-Cotes quadrature rules. This paper focused on constant and pantograph delay types, and the previous values are used to interpolate the delay solutions. Moreover, the studies also carried out on the stability analysis of the proposed method. Some numerical results are tested to validate the competency of the multistep block method with quadrature rule approach.