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3-Point Implicit Block Method for Solving Ordinary Differential Equations

Zanariah Abdul Majid, and Mohamed Bin Suleiman, and Zurni Omar, (2006) 3-Point Implicit Block Method for Solving Ordinary Differential Equations. Bulletin of the Malaysian Mathematical Sciences Society, 29 (1). pp. 23-31. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v29n1/v29n1p4.pdf

Affiliations

Universiti Putra Malaysia, Faculty of Science, Mathematics Dept.
University Utara Malaysia, Faculty of Quantitative Science

Abstract

A 3-point implicit block method for solving system of first order ordinary differential equations (ODEs) is proposed. This method approximates the solutions of initial value problems at 3 points simultaneously using variable step size. The stability of the method is also studied. The numerical results show that the method is more efficient than the 3-point implicit block method developed by Rosser [4] in terms of the total number of steps and execution times.


2000 Mathematics Subject Classification: 65L06, 65L05

Item Type:Journal
Keywords:3-point, implicit block method, ordinary differential equations.
Subjects:Q Science, Computer Science
ID Code:1430

[1] R. Bronson, Modern Introductory Differential Equation, Schaum’s Outline Series, McGraw- Hill, USA, 1973.

[2] W.E. Milne, Numerical Solution of Differential Equations, Wiley, New York, 1953.

[3] Zurni Omar, Developing parallel block methods for solving higher order ODEs directly, Thesis, University Putra Malaysia, Malaysia, 1999.

[4] J.B. Rosser, A Runge-Kutta for all seasons, SIAM Rev. 9 (1967), 417—452.

[5] L.F. Shampine and H.A. Watts, Block implicit one-step methods, Math. Comp. 23 (1969), 731—740.

[6] H.W. Tam, Two-stage parallel methods for the numerical solution of ordinary differential equations, SIAM J. Sci. Statist. Comput. 13(5) (1992), 1062—1084.

[7] P.B. Worland, Parallel methods for the numerical solution of ordinary differential equations, IEEE Trans. Computers C-25(10) (1976), 1045—1048.

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