Global error estimation for explicit second derivative general linear methods

Ali Abdi, Gholamreza Hojjati, Giuseppe Izzo, Zdzislaw Jackiewicz

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we describe an approach to estimate the global error for explicit second derivative general linear methods based on the approach which has been already used for global error estimation of explicit general linear methods. In this approach, to estimate the global error, we use the numerical solutions of pairs of second derivative general linear methods with the same order and stage order that are constructed such that their global error functions are proportional. Numerical experiments demonstrate the excellent agreement of the global error estimation with the exact one in both constant and variable stepsize environments.

Original languageEnglish (US)
JournalNumerical Algorithms
DOIs
StateAccepted/In press - 2021

Keywords

  • Fixed-stepsize methods
  • General linear methods
  • Global error estimation
  • Inherent Runge–Kutta stability
  • Ordinary differential equations
  • Second derivative methods

ASJC Scopus subject areas

  • Applied Mathematics

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