An a priori error analysis of the hp-version of the C0-continuous Petrov-Galerkin method for nonlinear second-order delay differential equations. Issue 8 (3rd August 2022)

• Record Type: Journal Article
• Authors: Wang, Lina; Wei, Yichen; Yi, Lijun
• Is Part Of: International journal of computer mathematics. Volume 99:Issue 8(2022)
• Page Start: 1557
• Page End: 1578
• Publication Date: 2022-08-03
• Subjects: Second-order delay differential equations -- hp-version -- continuous Petrov-Galerkin method -- time-stepping -- exponential convergence; 65L60 -- 65L05 -- 65L70; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2021.1993204
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : We study an hp -version of the C 0 -continuous Petrov-Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays. We derive a priori error bound in the H 1 -norm that is fully explicit in the local time steps, in the local approximation degrees, and in the local regularity indexes of the exact solutions. Moreover, we prove that the C 0 -continuous Petrov-Galerkin based on special hp -version discretization can yield exponential rates of convergence for analytic solutions with initial singularities. Numerical experiments are provided to illustrate the theoretical results.