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On the Order and Attainable Intervals of Periodicity of Explicit Nyström Methods for y″ = f(t,y)*

M. M. Chawla
SIAM Journal on Numerical Analysis
Vol. 22, No. 1 (Feb., 1985), pp. 127-131
Stable URL: http://www.jstor.org/stable/2156924
Page Count: 5
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On the Order and Attainable Intervals of Periodicity of Explicit Nyström Methods for y″ = f(t,y)*
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Abstract

We consider the class of m-stage explicit Nyström methods for y″ = f(t, y) which are at least order one. We first show that the length of the interval of periodicity (see our definition in § 2) scaled by dividing by m for any such method cannot exceed two. While there exist methods of order one and two possessing this optimal length of interval of periodicity, we show that if a method of order higher than two possesses an interval of periodicity, then the length of its scaled interval of periodicity is less than two.

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