Taylor collocation method for high-order neutral delay Volterra integro-differential equations

Abstract

In this paper, the Taylor collocation method is applied to numerically solve a kth-order neutral linear Volterra integro-differential equation with constant delay and variable coefficients.We also provide a rigorous analysis to estimate the difference between the exact and approximate solution and their derivatives up to order k-1. Numerical examples are included to prove the performance of the presented convergent algorithm.

The Implicit Multistep Block Method with An Off-step Point for Initial Value Problems of Neutral Delay Volterra Integro-differential Equations

“…A contribution to the topic of the paper and relevant literature is provided from the numerical examples for the uniformly asymptotically stability of zero solution as well as integrability and boundedness of solutions. [17] have more recently used the Taylor collocation method to numerically solve a k th -order NDVIDE with constant delay. The approach is simple to use, convergent, and accurate.…”