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Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations. 相似文献
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Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay toofast relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05. 相似文献
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An analogy is stressed between the order-parameter symmetries of the two-dimensional d-pairing wave superconductors and of liquid-crystal mesophases formed from achiral bent-shaped molecules. It leads to a definition of a class of liquid-crystal states which are the analogs of the unconventional superconducting states, and are characterized by a loss of discrete symmetry operations of the parent state. 相似文献
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Handzy DO Bauer W Daffin FC Gaff SJ Gelbke CK Glasmacher T Gualtieri E Hannuschke S Huang MJ Kunde GJ Lacey R Li T Lisa MA Llope WJ Lynch WG Martin L Montoya CP Pak R Peaslee GF Pratt S Schwarz C Stone N Tsang MB Vander Molen AM Westfall GD Yee J Yennello SJ 《Physical review letters》1995,75(16):2916-2919