## Communications in Applied Mathematics and Computational Science

### Legendre spectral-collocation method for Volterra integral differential equations with nonvanishing delay

#### Abstract

The main purpose of this paper is to propose the Legendre spectral-collocation method to solve the Volterra integral differential equations with nonvanishing delay which arise in many problems, such as modeling in biosciences and population. In our method we divide the definition domain of the solution into several subintervals where the solution is sufficiently smooth. Then we can use the spectral-collocation method for these equations in each subinterval. We provide convergence analysis for this method, which shows that the numerical errors decay exponentially. Numerical examples are presented to confirm these theoretical results.

#### Article information

Source
Commun. Appl. Math. Comput. Sci., Volume 8, Number 1 (2013), 67-98.

Dates
Revised: 28 August 2013
Accepted: 2 September 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.camcos/1513732080

Digital Object Identifier
doi:10.2140/camcos.2013.8.67

Mathematical Reviews number (MathSciNet)
MR3143819

Zentralblatt MATH identifier
1284.65189

#### Citation

Chen, Yanping; Gu, Zhendong. Legendre spectral-collocation method for Volterra integral differential equations with nonvanishing delay. Commun. Appl. Math. Comput. Sci. 8 (2013), no. 1, 67--98. doi:10.2140/camcos.2013.8.67. https://projecteuclid.org/euclid.camcos/1513732080

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