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Volume 11, Issue 2
Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay

Weishan Zheng, Yanping Chen & Yunqing Huang

Adv. Appl. Math. Mech., 11 (2019), pp. 486-500.

Published online: 2019-01

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  • Abstract

In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both $L^{2}$-norm and $L^{\infty}$-norm. In the end, the numerical experiment is illustrated to confirm the theoretical analysis.

  • Keywords

Convergence analysis, Legendre-spectral method, second order Volterra integro-differential equation, delay, error analysis.

  • AMS Subject Headings

65R20, 45E05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-486, author = {Zheng , WeishanChen , Yanping and Huang , Yunqing}, title = {Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {486--500}, abstract = {

In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both $L^{2}$-norm and $L^{\infty}$-norm. In the end, the numerical experiment is illustrated to confirm the theoretical analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0121}, url = {http://global-sci.org/intro/article_detail/aamm/12973.html} }
TY - JOUR T1 - Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay AU - Zheng , Weishan AU - Chen , Yanping AU - Huang , Yunqing JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 486 EP - 500 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0121 UR - https://global-sci.org/intro/article_detail/aamm/12973.html KW - Convergence analysis, Legendre-spectral method, second order Volterra integro-differential equation, delay, error analysis. AB -

In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both $L^{2}$-norm and $L^{\infty}$-norm. In the end, the numerical experiment is illustrated to confirm the theoretical analysis.

Weishan Zheng, Yanping Chen & Yunqing Huang. (2020). Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay. Advances in Applied Mathematics and Mechanics. 11 (2). 486-500. doi:10.4208/aamm.OA-2018-0121
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