### A numerical framework for solving high-order pantograph-delay Volterra integro-differential equations

Farshid Mirzaee, Saeed Bimesl, Emran Tohidi

#### Abstract

In this paper, we present an efficient numerical method to solve Volterra integrodifferentialequations of pantograph-delay type. We use the Euler polynomials toapproximate the solutions. The proposed method is discussed in detail and comparedby solving some numerical examples. Moreover, the error estimates of the proposedmethod is given. Special cases of the main results are also mentioned.

#### Keywords

Accuracy; euler polynomials; high-order; integro-differential equations; pantograph-delay.

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