Volume 8, Issue 2
A Chebyshev Spectral Collocation Method for Nonlinear Volterra Integral Equations with Vanishing Delays

Zhong-Qing Wang, Chang-Tao Sheng, Hong-Li Jia & Dao Li

East Asian J. Appl. Math., 8 (2018), pp. 233-260.

Published online: 2018-05

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  • Abstract

A multistep Chebyshev-Gauss-Lobatto spectral collocation method for nonlinear Volterra integral equations with vanishing delays is developed. The convergence of the hp-version of the method in supremum norm is proved. Numerical experiments show the efficiency of the method for equations with highly oscillating, steep gradient and non-smooth solutions.

  • Keywords

Multistep Chebyshev-Gauss-Lobatto spectral collocation method, nonlinear Volterra integral equation, vanishing variable delay.

  • AMS Subject Headings

65L60, 45D05, 41A10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-233, author = {}, title = {A Chebyshev Spectral Collocation Method for Nonlinear Volterra Integral Equations with Vanishing Delays}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {2}, pages = {233--260}, abstract = {

A multistep Chebyshev-Gauss-Lobatto spectral collocation method for nonlinear Volterra integral equations with vanishing delays is developed. The convergence of the hp-version of the method in supremum norm is proved. Numerical experiments show the efficiency of the method for equations with highly oscillating, steep gradient and non-smooth solutions.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130416.071217a}, url = {http://global-sci.org/intro/article_detail/eajam/12203.html} }
TY - JOUR T1 - A Chebyshev Spectral Collocation Method for Nonlinear Volterra Integral Equations with Vanishing Delays JO - East Asian Journal on Applied Mathematics VL - 2 SP - 233 EP - 260 PY - 2018 DA - 2018/05 SN - 8 DO - http://dor.org/10.4208/eajam.130416.071217a UR - https://global-sci.org/intro/article_detail/eajam/12203.html KW - Multistep Chebyshev-Gauss-Lobatto spectral collocation method, nonlinear Volterra integral equation, vanishing variable delay. AB -

A multistep Chebyshev-Gauss-Lobatto spectral collocation method for nonlinear Volterra integral equations with vanishing delays is developed. The convergence of the hp-version of the method in supremum norm is proved. Numerical experiments show the efficiency of the method for equations with highly oscillating, steep gradient and non-smooth solutions.

Zhong-Qing Wang, Chang-Tao Sheng, Hong-Li Jia & Dao Li. (2020). A Chebyshev Spectral Collocation Method for Nonlinear Volterra Integral Equations with Vanishing Delays. East Asian Journal on Applied Mathematics. 8 (2). 233-260. doi:10.4208/eajam.130416.071217a
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