Runge–Kutta type methods with special properties for the numerical integration of ordinary differential equations

Z Kalogiratou, T Monovasilis, G Psihoyios, TE Simos - Physics Reports, 2014 - Elsevier
In this work we review single step methods of the Runge–Kutta type with special properties.
Among them are methods specially tuned to integrate problems that exhibit a pronounced …

[PDF][PDF] Exponentially fitted symplectic Runge–Kutta–Nyström methods

T Monovasilis, Z Kalogiratou, TE Simos - Appl. Math. Inf. Sci, 2013 - naturalspublishing.com
In this work we consider symplectic Runge Kutta Nyström (SRKN) methods with three
stages. We construct a fourth order SRKN with constant coefficients and a trigonometrically …

[HTML][HTML] Construction of an optimized explicit Runge–Kutta–Nyström method for the numerical solution of oscillatory initial value problems

AA Kosti, ZA Anastassi, TE Simos - Computers & Mathematics with …, 2011 - Elsevier
Abstract An explicit optimized Runge–Kutta–Nyström method with four stages and fifth
algebraic order is developed. The produced method has variable coefficients with zero …

[HTML][HTML] On modified Runge–Kutta trees and methods

C Tsitouras, IT Famelis, TE Simos - Computers & Mathematics with …, 2011 - Elsevier
Modified Runge–Kutta (mRK) methods can have interesting properties as their coefficients
may depend on the step length. By a simple perturbation of very few coefficients we may …

Construction of exponentially fitted symplectic Runge–Kutta–Nyström methods from partitioned Runge–Kutta methods

T Monovasilis, Z Kalogiratou, TE Simos - Mediterranean Journal of …, 2016 - Springer
In this work, we give the general framework for constructing trigonometrically fitted
symplectic Runge–Kutta–Nyström (RKN) methods from symplectic trigonometrically fitted …

Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday

B Paternoster - Computer Physics Communications, 2012 - Elsevier
The standard monograph in this area is the book Exponential fitting by Ixaru and Vanden
Berghe (Kluwer, Boston-Dordrecht-London, 2004) but a fresh look on things is necessary …

Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods

A Tocino, J Vigo-Aguiar - Mathematical and Computer Modelling, 2005 - Elsevier
Symplectic Conditions for Exponential Fitting Runge-Kutta-NystrSm Methods Page 1 ELSEVIER
MATHEMATICAL Available online at www.sciencedirect.com 8CIENCE ~___~DIRECT e …

A symplectic exponentially fitted modified Runge–Kutta–Nyström method for the numerical integration of orbital problems

H Van de Vyver - New Astronomy, 2005 - Elsevier
A symplectic exponentially fitted modified Runge–Kutta–Nyström method for the numerical
integration of orbital problems - ScienceDirect Skip to main contentSkip to article Elsevier …

Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems

JM Franco - Computer Physics Communications, 2007 - Elsevier
A class of explicit modified Runge–Kutta–Nyström (RKN) methods for the numerical
integration of second-order IVPs with oscillatory solutions is presented. The symplecticness …

[HTML][HTML] Structure preservation of exponentially fitted Runge–Kutta methods

M Calvo, JM Franco, JI Montijano, L Rández - Journal of computational and …, 2008 - Elsevier
The preservation of some structure properties of the flow of differential systems by numerical
exponentially fitted Runge–Kutta (EFRK) methods is considered. A complete …