IJPAM: Volume 40, No. 4 (2007)

THE DIRECT SOLUTION OF $y''=f(x,y,y')$

Samuel N. Jator
Department of Mathematics
Austin Peay State University
Clarksville, TN 37044, USA
email: Jators@apsu.edu

Abstract.A linear multistep method (LMM)with continuous coefficients is considered and directly applied to solve second order initial value problems (IVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 6) which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block method and verifying that the block method is zero-stable and consistent. The superiority of the MFDMs over the methods in Awoyemi [#!AW01!#], [#!AWK!#] is established numerically.

Received: September 6, 2007

AMS Subject Classification: 65L05, 65L06, 65L12

Key Words and Phrases: second order initial value problems, multiple finite difference methods, block, zero-stability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 4