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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.

Yang , YinChen , YanpingHuang , Yunqing and Yang , Wei. (2018). 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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