On the generation of higher order numerical integration methods using lower order Adams-Bashforth and Adams-Moulton methods

J. C. Chiou, Shuen-De Wu

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper, a new explicit numerical integration method is proposed. The proposed method is based on the relationship that m-step Adams-Moulton method is the linear convex combination of (m-1)-step Adams-Moulton and m-step Adams-Bashforth methods with a fixed weighting coefficient. By examining the order of accuracy and stability regions, we conclude that the present method is superior to the traditional Adams-Bashforth-Moulton predictor-corrector method. A simple harmonic oscillator problem is used to demonstrate the efficiency of the proposed method.

Original languageEnglish
Pages (from-to)19-29
Number of pages11
JournalJournal of Computational and Applied Mathematics
Volume108
Issue number1-2
Publication statusPublished - 1999 Aug 15

Fingerprint

Numerical Integration Methods
Higher Order
Predictor-corrector Methods
Stability Region
Convex Combination
Harmonic Oscillator
Weighting
Linear Combination
Coefficient
Demonstrate

Keywords

  • Accuracy and stability analysis
  • Adams-Moulton and Adams-Bashforth numerical integrator

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{81bdba6420f94a909e502c11f6c27de8,
title = "On the generation of higher order numerical integration methods using lower order Adams-Bashforth and Adams-Moulton methods",
abstract = "In this paper, a new explicit numerical integration method is proposed. The proposed method is based on the relationship that m-step Adams-Moulton method is the linear convex combination of (m-1)-step Adams-Moulton and m-step Adams-Bashforth methods with a fixed weighting coefficient. By examining the order of accuracy and stability regions, we conclude that the present method is superior to the traditional Adams-Bashforth-Moulton predictor-corrector method. A simple harmonic oscillator problem is used to demonstrate the efficiency of the proposed method.",
keywords = "Accuracy and stability analysis, Adams-Moulton and Adams-Bashforth numerical integrator",
author = "Chiou, {J. C.} and Shuen-De Wu",
year = "1999",
month = "8",
day = "15",
language = "English",
volume = "108",
pages = "19--29",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - On the generation of higher order numerical integration methods using lower order Adams-Bashforth and Adams-Moulton methods

AU - Chiou, J. C.

AU - Wu, Shuen-De

PY - 1999/8/15

Y1 - 1999/8/15

N2 - In this paper, a new explicit numerical integration method is proposed. The proposed method is based on the relationship that m-step Adams-Moulton method is the linear convex combination of (m-1)-step Adams-Moulton and m-step Adams-Bashforth methods with a fixed weighting coefficient. By examining the order of accuracy and stability regions, we conclude that the present method is superior to the traditional Adams-Bashforth-Moulton predictor-corrector method. A simple harmonic oscillator problem is used to demonstrate the efficiency of the proposed method.

AB - In this paper, a new explicit numerical integration method is proposed. The proposed method is based on the relationship that m-step Adams-Moulton method is the linear convex combination of (m-1)-step Adams-Moulton and m-step Adams-Bashforth methods with a fixed weighting coefficient. By examining the order of accuracy and stability regions, we conclude that the present method is superior to the traditional Adams-Bashforth-Moulton predictor-corrector method. A simple harmonic oscillator problem is used to demonstrate the efficiency of the proposed method.

KW - Accuracy and stability analysis

KW - Adams-Moulton and Adams-Bashforth numerical integrator

UR - http://www.scopus.com/inward/record.url?scp=0032599423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032599423&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032599423

VL - 108

SP - 19

EP - 29

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1-2

ER -