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Volume 15, Issue 1-2
The $h$-$p$ Version of the Continuous Petrov-Galerkin Method for Nonlinear Volterra Functional Integro-Differential Equations with Vanishing Delays

Lijun Yi & Benqi Guo

Int. J. Numer. Anal. Mod., 15 (2018), pp. 26-47.

Published online: 2018-01

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  • Abstract

We investigate an $h$-$p$ version of the continuous Petrov-Galerkin method for the nonlinear Volterra functional integro-differential equations with vanishing delays. We derive $h$-$p$ version a priori error estimates in the $L^2$-, $H^1$- and $L^∞$-norms, which are completely explicit in the local discretization and regularity parameters. Numerical computations supporting the theoretical results are also presented.

  • Keywords

$h$-$p$ version, continuous Petrov-Galerkin method, nonlinear Volterra functional integro-differential equations, vanishing delays.

  • AMS Subject Headings

65L60, 65R20, 65L70, 41A10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ylj5152@shnu.edu.cn (Lijun Yi)

Benqi.Guo@umanitoba.ca (Benqi Guo)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-26, author = {Yi , Lijun and Guo , Benqi}, title = {The $h$-$p$ Version of the Continuous Petrov-Galerkin Method for Nonlinear Volterra Functional Integro-Differential Equations with Vanishing Delays}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {1-2}, pages = {26--47}, abstract = {

We investigate an $h$-$p$ version of the continuous Petrov-Galerkin method for the nonlinear Volterra functional integro-differential equations with vanishing delays. We derive $h$-$p$ version a priori error estimates in the $L^2$-, $H^1$- and $L^∞$-norms, which are completely explicit in the local discretization and regularity parameters. Numerical computations supporting the theoretical results are also presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10554.html} }
TY - JOUR T1 - The $h$-$p$ Version of the Continuous Petrov-Galerkin Method for Nonlinear Volterra Functional Integro-Differential Equations with Vanishing Delays AU - Yi , Lijun AU - Guo , Benqi JO - International Journal of Numerical Analysis and Modeling VL - 1-2 SP - 26 EP - 47 PY - 2018 DA - 2018/01 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10554.html KW - $h$-$p$ version, continuous Petrov-Galerkin method, nonlinear Volterra functional integro-differential equations, vanishing delays. AB -

We investigate an $h$-$p$ version of the continuous Petrov-Galerkin method for the nonlinear Volterra functional integro-differential equations with vanishing delays. We derive $h$-$p$ version a priori error estimates in the $L^2$-, $H^1$- and $L^∞$-norms, which are completely explicit in the local discretization and regularity parameters. Numerical computations supporting the theoretical results are also presented.

Lijun Yi & Benqi Guo. (2020). The $h$-$p$ Version of the Continuous Petrov-Galerkin Method for Nonlinear Volterra Functional Integro-Differential Equations with Vanishing Delays. International Journal of Numerical Analysis and Modeling. 15 (1-2). 26-47. doi:
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