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Volume 19, Issue 4
Extrapolation and A-Posteriori Error Estimators of Petrov-Galerkin Methods for Non-Linear Volterra Integro-Differential Equations

Shu-Hua Zhang, Tao Lin, Yan-Ping Lin & Ming Rao

J. Comp. Math., 19 (2001), pp. 407-422.

Published online: 2001-08

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  • Abstract

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

  • Keywords

Volterra integro-differential equations, Petrov-Galerkin finite element methods, Asymptotic expansions, Interpolation post-processing, A-posteriori error estimators.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-407, author = {Zhang , Shu-HuaLin , TaoLin , Yan-Ping and Rao , Ming}, title = {Extrapolation and A-Posteriori Error Estimators of Petrov-Galerkin Methods for Non-Linear Volterra Integro-Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {4}, pages = {407--422}, abstract = {

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8993.html} }
TY - JOUR T1 - Extrapolation and A-Posteriori Error Estimators of Petrov-Galerkin Methods for Non-Linear Volterra Integro-Differential Equations AU - Zhang , Shu-Hua AU - Lin , Tao AU - Lin , Yan-Ping AU - Rao , Ming JO - Journal of Computational Mathematics VL - 4 SP - 407 EP - 422 PY - 2001 DA - 2001/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8993.html KW - Volterra integro-differential equations, Petrov-Galerkin finite element methods, Asymptotic expansions, Interpolation post-processing, A-posteriori error estimators. AB -

In this paper we will show that the Richardson extrapolation can be used to enhance the numerical solution generated by a Petrov-Galerkin finite element method for the initial-value problem for a nonlinear Volterra integro-differential equation. As by-products, we will also show that these enhanced approximations can be used to form a class of a-posteriori estimators for this Petrov-Galerkin finite element method. Numerical examples are supplied to illustrate the theoretical results.

Zhang , Shu-HuaLin , TaoLin , Yan-Ping and Rao , Ming. (2001). Extrapolation and A-Posteriori Error Estimators of Petrov-Galerkin Methods for Non-Linear Volterra Integro-Differential Equations. Journal of Computational Mathematics. 19 (4). 407-422. doi:
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