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Home  >  volume 36 (no1)

Scheme Formulation Techniques for Direct Integration of General Third Order ODEs by Z A. Adegboye, Abubakar Saddiq Magaji and Mohammed Ibrahim (Pages 15-22)
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Formulation of a stable implicit scheme for direct integration of general third order ordinary differential equations (ODEs) by using Runge-Kutta–Nystrom and Linear Multistep techniques was presented. Runge-Kutta Type scheme was obtained by the evaluation of the continuous interpolant at different nodes of polynomial which was converted to Implicit Runge-Kutta Type Method for direct integration of general third order ordinary differential equations(ODEs) by using the direct method as those invented by Nystrom. The approach of collocation method approximation was adopted in the derivation of discrete Linear Multistep scheme and extended to the case in which the approximate solution to a second order (special or general), as well as first order Initial Value Problems(IVPs) can be calculated  from the same continuous interpolant. Both method are of the same nodes of  polynomial, order and has an implicit structure for efficient implementation. The convergence of the methods is achieved as shown in the table of results.

                Keywords: Runge-Kutta-Nystrom, Collocation method, Continuous interpolant, Nodes of polynomial and Implicit Structure