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Volume 7, Issue 1
Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

Yin Yang, Yanping Chen, Yunqing Huang & Wei Yang

DOI: 10.4208/aamm.2013.m163

Adv. Appl. Math. Mech., 7 (2015), pp. 74-88.

Published online: 2018-03

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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 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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@Article{AAMM-7-74, author = {Yang , YinChen , YanpingHuang , Yunqing and Yang , Wei}, title = {Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {1}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m163}, url = {http://global-sci.org/intro/article_detail/aamm/10945.html} }
TY - JOUR T1 - Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations AU - Yang , Yin AU - Chen , Yanping AU - Huang , Yunqing AU - Yang , Wei JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 74 EP - 88 PY - 2018 DA - 2018/03 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m163 UR - https://global-sci.org/intro/article_detail/aamm/10945.html KW - AB -

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.

Yin Yang, Yanping Chen, Yunqing Huang & Wei Yang. (1970). Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations. Advances in Applied Mathematics and Mechanics. 7 (1). 74-88. doi:10.4208/aamm.2013.m163
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