A variable step implicit block multistep method for solving first-order ODEs

Siamak Mehrkanoon; Zanariah Abdul Majid; Mohamed Suleiman

doi:10.1016/j.cam.2009.10.023

A variable step implicit block multistep method for solving first-order ODEs

Siamak Mehrkanoon
, Zanariah Abdul Majid
, Mohamed Suleiman

Sub Algorithmic Data Analysis

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

A new four-point implicit block multistep method is developed for solving systems of
first-order ordinary differential equations with variable step size. The method computes
the numerical solution at four equally spaced points simultaneously. The stability
of the proposed method is investigated. The Gauss–Seidel approach is used for the
implementation of the proposed method in the PE(CE)
m mode. The method is presented
in a simple form of Adams type and all coefficients are stored in the code in order to avoid
the calculation of divided difference and integration coefficients. Numerical examples are
given to illustrate the efficiency of the proposed method

Original language	Undefined/Unknown
Article number	9
Pages (from-to)	2387-2394
Number of pages	8
Journal	J. Comput. Appl. Math.
Volume	233
Issue number	9
DOIs	https://doi.org/10.1016/j.cam.2009.10.023
Publication status	Published - 2010

Bibliographical note

DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

Keywords

Block method
Variable step size
Ordinary differential equations

Access to Document

10.1016/j.cam.2009.10.023

Cite this

@article{8fef40fd56ee459b91162a8f3b5ae5a0,

title = "A variable step implicit block multistep method for solving first-order ODEs",

abstract = "A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss–Seidel approach is used for the implementation of the proposed method in the PE(CE) m mode. The method is presented in a simple form of Adams type and all coefficients are stored in the code in order to avoid the calculation of divided difference and integration coefficients. Numerical examples are given to illustrate the efficiency of the proposed method",

keywords = "Block method, Variable step size, Ordinary differential equations",

author = "Siamak Mehrkanoon and Majid, \{Zanariah Abdul\} and Mohamed Suleiman",

note = "DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.",

year = "2010",

doi = "10.1016/j.cam.2009.10.023",

language = "Undefined/Unknown",

volume = "233",

pages = "2387--2394",

journal = "J. Comput. Appl. Math.",

publisher = "Elsevier BV",

number = "9",

}

TY - JOUR

T1 - A variable step implicit block multistep method for solving first-order ODEs

AU - Mehrkanoon, Siamak

AU - Majid, Zanariah Abdul

AU - Suleiman, Mohamed

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2010

Y1 - 2010

N2 - A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss–Seidel approach is used for the implementation of the proposed method in the PE(CE) m mode. The method is presented in a simple form of Adams type and all coefficients are stored in the code in order to avoid the calculation of divided difference and integration coefficients. Numerical examples are given to illustrate the efficiency of the proposed method

AB - A new four-point implicit block multistep method is developed for solving systems of first-order ordinary differential equations with variable step size. The method computes the numerical solution at four equally spaced points simultaneously. The stability of the proposed method is investigated. The Gauss–Seidel approach is used for the implementation of the proposed method in the PE(CE) m mode. The method is presented in a simple form of Adams type and all coefficients are stored in the code in order to avoid the calculation of divided difference and integration coefficients. Numerical examples are given to illustrate the efficiency of the proposed method

KW - Block method

KW - Variable step size

KW - Ordinary differential equations

U2 - 10.1016/j.cam.2009.10.023

DO - 10.1016/j.cam.2009.10.023

M3 - Article

VL - 233

SP - 2387

EP - 2394

JO - J. Comput. Appl. Math.

JF - J. Comput. Appl. Math.

IS - 9

M1 - 9

ER -