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

Published online by Cambridge University Press:  09 January 2015

Yin Yang ,
Yanping Chen ,
Yunqing Huang  and
Wei Yang
Yin Yang
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
Yanping Chen*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
Yunqing Huang
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
Wei Yang
Affiliation:
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
*
*Email:yangyinxtu@xtu.edu.cn(Y. Yang), yanpingchen@scnu.edu.cn(Y. Chen), huangyq@xtu.edu.cnY. Huang, yangweixtu@126.com(W. Yang)
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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 indicate that the numerical errors in L2-norm and L∞-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.

Keywords

65R2045J0565N12Spectral methodnonlinearVolterra integral equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 1 , February 2015 , pp. 74 - 88
Copyright
Copyright © Global Science Press Limited 2015 

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