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Volume 4, Issue 3
Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations

Yunxia Wei & Yanping Chen

DOI: 10.4208/nmtma.2011.m1028

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 419-438.

Published online: 2011-04

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  • Abstract

A class of numerical methods is developed for second order Volterra integro-differential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the $L^\infty$-norm and $L^2$-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods.

  • Keywords

Second order Volterra integro-differential equations, Gauss quadrature formula, Legendre-collocation methods, convergence analysis.

  • AMS Subject Headings

45L10, 65R20, 65D15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-419, author = {Yunxia Wei and Yanping Chen}, title = {Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {3}, pages = {419--438}, abstract = {

A class of numerical methods is developed for second order Volterra integro-differential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the $L^\infty$-norm and $L^2$-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1028}, url = {http://global-sci.org/intro/article_detail/nmtma/5976.html} }
TY - JOUR T1 - Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations AU - Yunxia Wei & Yanping Chen JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 419 EP - 438 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1028 UR - https://global-sci.org/intro/article_detail/nmtma/5976.html KW - Second order Volterra integro-differential equations, Gauss quadrature formula, Legendre-collocation methods, convergence analysis. AB -

A class of numerical methods is developed for second order Volterra integro-differential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the $L^\infty$-norm and $L^2$-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods.

Yunxia Wei and Yanping Chen. (2011). Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 4 (3). 419-438. doi:10.4208/nmtma.2011.m1028
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