Author:
Chawla M. M.,Sharma S. R.
Abstract
AbstractIn this paper all three-stage third order (explicit) Runge-Kutta-Nyström (R-K-N) methods for y″ = f (x, y, y′) are presented. While determining particular methods we require that when these methods are applied to the test equation: y″ − (α + β) y ′ + αβy = 0, the measure of the relative error F, introduced by Rutishauser [4], should not deteriorate in the case of equal eigenvalues (β → α). Further, we require that when these methods are applied to special differential equations y″ = f(x, y) they should possess either of the two properties: (P1) a method remains of order three but is two-stage, (P2) a method remains three-stage but attains order four. We present new R-K-N methods which are stabilized in the sense of Ruthishauser [4] and which possess the property (P1). (There does not exist any three-stage third order R-K-N method which is stabilized and which possesses the property (P2).)
Publisher
Cambridge University Press (CUP)
Cited by
21 articles.
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