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