Volume 5, Issue 2
A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay

Adv. Appl. Math. Mech., 5 (2013), pp. 131-145.

Published online: 2013-05

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• Abstract

In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with pantograph 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 $L^∞$-norm.

• Keywords

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

65R20, 34K28

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• TXT
@Article{AAMM-5-131, author = {Weishan and Zheng and and 20146 and and Weishan Zheng and Yanping and Chen and and 20147 and and Yanping Chen}, title = {A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {2}, pages = {131--145}, abstract = {

In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with pantograph 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 $L^∞$-norm.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m1209}, url = {http://global-sci.org/intro/article_detail/aamm/61.html} }
TY - JOUR T1 - A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay AU - Zheng , Weishan AU - Chen , Yanping JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 131 EP - 145 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.12-m1209 UR - https://global-sci.org/intro/article_detail/aamm/61.html KW - Legendre-spectral method, second order Volterra integro-differential equation, pantograph delay, error analysis. AB -

In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with pantograph 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 $L^∞$-norm.

Weishan Zheng & Yanping Chen. (1970). A Spectral Method for Second Order Volterra Integro-Differential Equation with Pantograph Delay. Advances in Applied Mathematics and Mechanics. 5 (2). 131-145. doi:10.4208/aamm.12-m1209
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