求解二阶刚性微分方程的对角隐式Runge-Kutta-Nystrm方法(英文)

Two-stage Diagonally-Implicit Runge-Kutta-Nystrm Methods for Stiff Second-order Differential Equations

在本文中,主要研究二级三阶对角隐式Runge-Kutta-Nystrm(DIRKN)方法关于二阶刚性常微分方程的R-稳定性,P-稳定性以及相延迟性质.我们获得了该方法的R-稳定域,并构造了R-稳定的二级三阶、相延迟阶为四阶的DIRKN方法.P-稳定的二级三阶DIRKN方法被证明是不存在的.我们还构造了相延迟阶为6阶和8阶的二级三阶DIRKN方法,但是这些方法不是R-稳定的.这推广了文献中的单对角隐式Runge-Kutta-Nystrm(SDIRKN)方法的相关结果.

In this paper,R-stability,P-stability and dispersive property of two-stage diagonally-implicit Runge-Kutta-Nystrm（DIRKN） methods for stiff second-order ordinary differential equations are discussed.The R-stable regions are obtained,and some R-stable two-stage DIRKN methods of order three and dispersive order four are constructed.It is shown that the P-stable two-stage DIRKN methods of order three do not exist.The two-stage DIRKN methods of order three and dispersive orders six and eight are constructed,but are not R-stable.These extend the corresponding results of the two-stage singly DIRKN methods in some references.