On Spectral Methods for Volterra Integral Equations and the Convergence Analysis

On Spectral Methods for Volterra Integral Equations and the Convergence Analysis

Year:    2008

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 6 : pp. 825–837

Abstract

The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach (with theoretical justification) for the Volterra type equations.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2008-JCM-8662

Journal of Computational Mathematics, Vol. 26 (2008), Iss. 6 : pp. 825–837

Published online:    2008-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Legendre-spectral method Second kind Volterra integral equation Convergence analysis.