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 - <p style="text-align: justify;">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.</p>