Τίτλος:
New family for Runge-Kutta-Nyström pairs of orders 6(4) with coefficients trained to address oscillatory problems
Γλώσσες Τεκμηρίου:
Αγγλικά
Περίληψη:
In this paper, we consider the integration of the special second-order initial value problem (IVP) (Formula presented.) by Runge-Kutta-Nyström (RKN) pairs of algebraic orders 6 and 4. For achieving this, we have to solve a certain set of order conditions. The main contribution of the present work is that we introduce a new methodology of solving them that possesses nine free parameters instead of four used by similar pairs until now. This family uses the FSAL (first stage as last) devise. Selecting these extra coefficients properly we may construct methods with better properties. Here, we exploit the free parameters in order to derive a pair with coefficients trained to furnish better results on problems with periodic solutions. Extensive numerical tests justify our approach. © 2022 John Wiley & Sons, Ltd.
Συγγραφείς:
Kovalnogov, V.N.
Kornilova, M.I.
Khakhalev, Y.A.
Generalov, D.A.
Simos, T.E.
Tsitouras, C.
Περιοδικό:
Mathematical Methods in the Applied Sciences
Εκδότης:
John Wiley and Sons Ltd
Λέξεις-κλειδιά:
Runge Kutta methods, Algebraic order; Free parameters; Initial-value problem; Numerical solution; Order conditions; Periodic problems; Property; Runge-kuttum-nystrom; Second-order initial value problems; Special second orders, Initial value problems
