Acta Mathematica Scientia

, Volume 39, Issue 2, pp 607–617

# Numerical Analysis for Volterra Integral Equation with Two Kinds of Delay

Article

## Abstract

In this article, we study the Volterra integral equations with two kinds of delay that are proportional delay and nonproportional delay. We mainly use Chebyshev spectral collocation method to analyze them. First, we use variable transformation to transform the equation into an new equation which is defined in [−1, 1]. Then, with the help of Gronwall inequality and some other lemmas, we provide a rigorous error analysis for the proposed method, which shows that the numerical error decay exponentially in L and $$L_{\omega ^c }^2$$-norm. In the end, we give numerical test to confirm the conclusion.

## Key words

Volterra integral equation proportional delay nonproportional delay linear transformation Chebyshev spectral-collocation method Gronwall inequality

65R20 45E05

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