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Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations
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Year:    2015

Author:    Yin Yang, Yanping Chen, Yunqing Huang, Wei Yang

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 1 : pp. 74–88

Abstract

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors in $L^2$-norm and  $L^\infty$-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2013.m163

Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 1 : pp. 74–88

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:   

Author Details

Yin Yang

Yanping Chen

Yunqing Huang

Wei Yang

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