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Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations

Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations
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Year:    2011

Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 3 : pp. 419–438

Abstract

A class of numerical methods is developed for second order Volterra integro-differential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the $L^\infty$-norm and $L^2$-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2011.m1028

Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 3 : pp. 419–438

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Second order Volterra integro-differential equations Gauss quadrature formula Legendre-collocation methods convergence analysis.

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