Vol. 8, No. 1, 2013

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

Yanping Chen and Zhendong Gu

Vol. 8 (2013), No. 1, 67–98

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.

Volterra integral differential equations, nonvanishing delay, Legendre spectral-collocation method, convergence analysis
Physics and Astronomy Classification Scheme
Primary: 65M70
Secondary: 45D05, 45J05
Received: 17 November 2012
Revised: 28 August 2013
Accepted: 2 September 2013
Published: 15 December 2013
Yanping Chen
School of Mathematics Science
South China Normal University
Guangzhou 510631
Zhendong Gu
School of Mathematics and Computational Science
Xiangtan University
Xiangtan 411105, Hunan