The $h$-$p$ Version of the Continuous Petrov-Galerkin Method for Nonlinear Volterra Functional Integro-Differential Equations with Vanishing Delays
Year: 2018
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-10554
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 1-2 : pp. 26–47
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: $h$-$p$ version continuous Petrov-Galerkin method nonlinear Volterra functional integro-differential equations vanishing delays.