Two Step Runge-Kutta-Nyström Methods for Oscillatory Problems Based on Mixed Polynomials

Abstract

Abstract. We consider two step Runge-Kutta-Nyström methods for the numerical integration of y = f (x, y) having periodic or oscillatory solutions. We assume that the frequency ω can be estimated in advance. Using the linear stage representation, we describe how to derive two step Runge-Kutta-Nyström methods which integrate trigonometric and mixed polynomials exactly. The resulting methods depend on the parameter ν = ωh, where h is the stepsize.

Vandermonde–Type Matrices in Two Step Collocation Methods for Special Second Order Ordinary Differential Equations

“…We extend the procedure indicated in [4], to obtain a general family of two step collocation methods for (1) within the family of two step Runge-KuttaNyström (TSRKN) methods, introduced in [8,9], providing numerical approximetions not only for the solution, but also to its first derivative at the step point.…”

Υπολογιστικές Μέθοδοι Συνήθων Διαφορικών Εξισώσεων Με Περιοδική Συμπεριφορά Της Λύσης

“…Στο πρόσφατο παρελθόν, αναπτύχθηκαν πλήθος μεθόδων Runge-Kutta αυτής της μορφής [8,9,11,12,35,86,87,114,116,120,128,140,158]. Αντίστοιχα, πολλές εφαρμογές έγιναν σε μεθόδους Runge-Kutta-Nyström [64,65,73,76,105,109,126,197,198,199,201,204].…”