Volume 51, Issue 2
Chebyshev Spectral Method for Volterra Integral Equation with Multiple Delays

Weishan Zheng & Yanping Chen

J. Math. Study, 51 (2018), pp. 214-226.

Published online: 2018-06

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  • Abstract

Numerical analysis is carried out for the Volterra integral equation with multiple delays in this article. Firstly, we make two variable transformations. Then we use the Gauss quadrature formula to get the approximate solutions. And then with the Chebyshev spectral method, the Gronwall inequality and some relevant lemmas, a rigorous analysis is provided. The conclusion is that the numerical error decay exponentially in $L^∞$ space and $L^2_{ω^c}$ space. Finally, numerical examples are given to show the feasibility and effectiveness of the Chebyshev spectral method.

  • AMS Subject Headings

65R20, 45E05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

weishanzheng@yeah.net (Weishan Zheng)

yanpingchen@scnu.edu.cn (Yanping Chen)

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@Article{JMS-51-214, author = {Zheng , Weishan and Chen , Yanping}, title = {Chebyshev Spectral Method for Volterra Integral Equation with Multiple Delays}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {51}, number = {2}, pages = {214--226}, abstract = {

Numerical analysis is carried out for the Volterra integral equation with multiple delays in this article. Firstly, we make two variable transformations. Then we use the Gauss quadrature formula to get the approximate solutions. And then with the Chebyshev spectral method, the Gronwall inequality and some relevant lemmas, a rigorous analysis is provided. The conclusion is that the numerical error decay exponentially in $L^∞$ space and $L^2_{ω^c}$ space. Finally, numerical examples are given to show the feasibility and effectiveness of the Chebyshev spectral method.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v51n2.18.06}, url = {http://global-sci.org/intro/article_detail/jms/12464.html} }
TY - JOUR T1 - Chebyshev Spectral Method for Volterra Integral Equation with Multiple Delays AU - Zheng , Weishan AU - Chen , Yanping JO - Journal of Mathematical Study VL - 2 SP - 214 EP - 226 PY - 2018 DA - 2018/06 SN - 51 DO - http://doi.org/10.4208/jms.v51n2.18.06 UR - https://global-sci.org/intro/article_detail/jms/12464.html KW - Volterra integral equation, multiple delays, Chebyshev spectral method, Gronwall inequality, convergence analysis. AB -

Numerical analysis is carried out for the Volterra integral equation with multiple delays in this article. Firstly, we make two variable transformations. Then we use the Gauss quadrature formula to get the approximate solutions. And then with the Chebyshev spectral method, the Gronwall inequality and some relevant lemmas, a rigorous analysis is provided. The conclusion is that the numerical error decay exponentially in $L^∞$ space and $L^2_{ω^c}$ space. Finally, numerical examples are given to show the feasibility and effectiveness of the Chebyshev spectral method.

Zheng , Weishan and Chen , Yanping. (2018). Chebyshev Spectral Method for Volterra Integral Equation with Multiple Delays. Journal of Mathematical Study. 51 (2). 214-226. doi:10.4208/jms.v51n2.18.06
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