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Volume 51, Issue 1
A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations

Hua Wu, Yunzhen Zhu, Hailu Wang & Lingfang Xu

DOI: 10.4208/jms.v51n1.18.04

J. Math. Study, 51 (2018), pp. 57-75.

Published online: 2018-04

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  • Abstract

We develop a domain decomposition Chebyshev spectral collocation method for the second-kind linear and nonlinear Volterra integral equations with smooth kernel functions. The method is easy to implement and possesses high accuracy. In the convergence analysis, we derive the spectral convergence order under the $L^∞$-norm without the Chebyshev weight function, and we also show numerical examples which coincide with the theoretical analysis.

  • Keywords

Nonlinear Volterra integral equations, domain decomposition method, Chebyshev–collocation spectral method, convergence analysis.

  • AMS Subject Headings

45D05, 45G10, 41A10, 65L60, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hwu@staff.shu.edu.cn (Hua Wu)

851747515@qq.com (Yunzhen Zhu)

18817612781@163.com (Hailu Wang)

xuhaishui@126.com (Lingfang Xu)

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@Article{JMS-51-57, author = {Wu , HuaZhu , YunzhenWang , Hailu and Xu , Lingfang}, title = {A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {51}, number = {1}, pages = {57--75}, abstract = {

We develop a domain decomposition Chebyshev spectral collocation method for the second-kind linear and nonlinear Volterra integral equations with smooth kernel functions. The method is easy to implement and possesses high accuracy. In the convergence analysis, we derive the spectral convergence order under the $L^∞$-norm without the Chebyshev weight function, and we also show numerical examples which coincide with the theoretical analysis.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v51n1.18.04}, url = {http://global-sci.org/intro/article_detail/jms/11315.html} }
TY - JOUR T1 - A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations AU - Wu , Hua AU - Zhu , Yunzhen AU - Wang , Hailu AU - Xu , Lingfang JO - Journal of Mathematical Study VL - 1 SP - 57 EP - 75 PY - 2018 DA - 2018/04 SN - 51 DO - http://doi.org/10.4208/jms.v51n1.18.04 UR - https://global-sci.org/intro/article_detail/jms/11315.html KW - Nonlinear Volterra integral equations, domain decomposition method, Chebyshev–collocation spectral method, convergence analysis. AB -

We develop a domain decomposition Chebyshev spectral collocation method for the second-kind linear and nonlinear Volterra integral equations with smooth kernel functions. The method is easy to implement and possesses high accuracy. In the convergence analysis, we derive the spectral convergence order under the $L^∞$-norm without the Chebyshev weight function, and we also show numerical examples which coincide with the theoretical analysis.

Hua Wu, Yunzhen Zhu, Hailu Wang & Lingfang Xu. (2019). A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations. Journal of Mathematical Study. 51 (1). 57-75. doi:10.4208/jms.v51n1.18.04
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