Derivation of continuous explicit two-step Runge-Kutta methods of order three

Z. Bartoszewski, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We describe a construction of continuous extensions to a new representation of two-step Runge-Kutta methods for ordinary differential equations. This representation makes possible the accurate and reliable estimation of local discretization error, facilitates the efficient implementation of these methods in variable stepsize environment, and adapts readily to the numerical solution of a class of delay differential equations. A number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state-of-the-art dde23 code from Matlab.

Original languageEnglish (US)
Pages (from-to)764-776
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume205
Issue number2
DOIs
StatePublished - Aug 15 2007

Fingerprint

Two-step Runge-Kutta Methods
Runge Kutta methods
Explicit Methods
Ordinary differential equations
Differential equations
Continuous Extension
Variable Step Size
Robust Performance
Discretization Error
Interpolants
Delay Differential Equations
Efficient Implementation
MATLAB
Ordinary differential equation
Numerical Solution

Keywords

  • Continuous interpolants
  • Nordsieck representation
  • Ordinary and delay differential equations
  • Two-step Runge-Kutta methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Derivation of continuous explicit two-step Runge-Kutta methods of order three. / Bartoszewski, Z.; Jackiewicz, Zdzislaw.

In: Journal of Computational and Applied Mathematics, Vol. 205, No. 2, 15.08.2007, p. 764-776.

Research output: Contribution to journalArticle

@article{417359151a6a4943b8e5f6d7deb78c4f,
title = "Derivation of continuous explicit two-step Runge-Kutta methods of order three",
abstract = "We describe a construction of continuous extensions to a new representation of two-step Runge-Kutta methods for ordinary differential equations. This representation makes possible the accurate and reliable estimation of local discretization error, facilitates the efficient implementation of these methods in variable stepsize environment, and adapts readily to the numerical solution of a class of delay differential equations. A number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state-of-the-art dde23 code from Matlab.",
keywords = "Continuous interpolants, Nordsieck representation, Ordinary and delay differential equations, Two-step Runge-Kutta methods",
author = "Z. Bartoszewski and Zdzislaw Jackiewicz",
year = "2007",
month = "8",
day = "15",
doi = "10.1016/j.cam.2006.02.056",
language = "English (US)",
volume = "205",
pages = "764--776",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Derivation of continuous explicit two-step Runge-Kutta methods of order three

AU - Bartoszewski, Z.

AU - Jackiewicz, Zdzislaw

PY - 2007/8/15

Y1 - 2007/8/15

N2 - We describe a construction of continuous extensions to a new representation of two-step Runge-Kutta methods for ordinary differential equations. This representation makes possible the accurate and reliable estimation of local discretization error, facilitates the efficient implementation of these methods in variable stepsize environment, and adapts readily to the numerical solution of a class of delay differential equations. A number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state-of-the-art dde23 code from Matlab.

AB - We describe a construction of continuous extensions to a new representation of two-step Runge-Kutta methods for ordinary differential equations. This representation makes possible the accurate and reliable estimation of local discretization error, facilitates the efficient implementation of these methods in variable stepsize environment, and adapts readily to the numerical solution of a class of delay differential equations. A number of numerical tests carried out on the obtained methods of order 3 with quadratic interpolants show their efficiency and robust performance which allow them to compete with the state-of-the-art dde23 code from Matlab.

KW - Continuous interpolants

KW - Nordsieck representation

KW - Ordinary and delay differential equations

KW - Two-step Runge-Kutta methods

UR - http://www.scopus.com/inward/record.url?scp=34248185042&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248185042&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2006.02.056

DO - 10.1016/j.cam.2006.02.056

M3 - Article

AN - SCOPUS:34248185042

VL - 205

SP - 764

EP - 776

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -