IJPAM: Volume 82, No. 3 (2013)

A SELF-STARTING LINEAR MULTISTEP METHOD FOR
DIRECT SOLUTION OF INITIAL VALUE
PROBLEMS OF SECOND ORDER ORDINARY
DIFFERENTIAL EQUATIONS

E.A. Areo$^1$, R.B. Adeniyi$^2$
$^1$Department of Mathematical Sciences
Federal University of Technology Akure
Akure, NIGERIA
$^2$Department of Mathematics
University of Ilorin
NIGERIA


Abstract. A Multistep collocation technique is used in this paper for direct solution of second order ordinary differential equations. The approach is used to obtain Multiple Finite Differential Methods (MFDMs) which are combined as simultaneous numerical integrators to form some block methods which are self-starting. The Stability and Convergence of the block methods are investigated, and the methods are found to be zero-stable, consistent and hence convergent. The block methods derived are tested on standard electric circuit and mechanical problems to illustrate the accuracy and desirability of our new method.

Received: June 4, 2012

AMS Subject Classification: 65L05, 65L06, 65L07, 65L20

Key Words and Phrases: multistep, collocation, multiple finite differential methods, simultaneous numerical integrators, block, self-starting, accuracy, consistent and convergent

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 82
Issue: 3