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

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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

Keywords

Block method
Variable step size
Ordinary differential equations

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10.1016/j.cam.2009.10.023

Cite this

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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 offirst-order ordinary differential equations with variable step size. The method computesthe numerical solution at four equally spaced points simultaneously. The stabilityof the proposed method is investigated. The Gauss–Seidel approach is used for theimplementation of the proposed method in the PE(CE)m mode. The method is presentedin a simple form of Adams type and all coefficients are stored in the code in order to avoidthe calculation of divided difference and integration coefficients. Numerical examples aregiven 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",

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AU - Mehrkanoon, Siamak

AU - Majid, Zanariah Abdul

AU - Suleiman, Mohamed

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PY - 2010

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

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

KW - Block method

KW - Variable step size

KW - Ordinary differential equations

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