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Applied Mathematics and Information Sciences, ISSN 1935-0090, 01/2013, Volume 7, Issue 1, pp. 81 - 85
In this work we consider symplectic Runge Kutta Nystrom (SRKN) methods with three stages. We construct a fourth order SRKN with constant coefficients and a... 
Symplectic methods | Exponential fitting | Runge kutta nyström methods | exponential fitting | NUMERICAL-INTEGRATION | symplectic methods | PHYSICS, MATHEMATICAL | Runge Kutta Nystrom methods
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 08/2016, Volume 13, Issue 4, pp. 2271 - 2285
In this work, we give the general framework for constructing trigonometrically fitted symplectic Runge-Kutta-Nystrom (RKN) methods from symplectic... 
65L05 | Runge-Kutta-Nystrom methods | MATHEMATICS | Hamiltonian systems | MATHEMATICS, APPLIED | FREQUENCY EVALUATION | Partitioned Runge-Kutta methods | ODES | NUMERICAL-INTEGRATION | symplectic methods | trigonometrical fitting | OSCILLATING SOLUTIONS | INITIAL-VALUE PROBLEMS | Computer science | International trade | Methods | Resveratrol
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2018, Volume 323, pp. 204 - 219
In this paper, we develop continuous-stage Runge–Kutta–Nyström (csRKN) methods for numerical integration of second-order ordinary differential equations (ODEs)... 
Symplecticity-preserving | Hamiltonian systems | Continuous-stage Runge–Kutta–Nyström methods | Symplectic conditions | Legendre polynomial | MATHEMATICS, APPLIED | Continuous-stage Runge-Kutta-Nystrom | methods | HAMILTONIAN-SYSTEMS | CONSTRUCTION | ODES
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 6, pp. 1639 - 1647
In this work we construct new Runge–Kutta–Nyström methods especially designed to integrate exactly the test equation y ″ = − w 2 y . We modify two existing... 
Runge–Kutta–Nyström methods | Exponential fitting | Schrödinger equation | Runge-Kutta-Nystrom methods | ORDER | MATHEMATICS, APPLIED | Schrodinger equation | OSCILLATING SOLUTIONS | FORMULAS | INITIAL-VALUE PROBLEMS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2019, Volume 361, pp. 670 - 679
On the basis of the previous work by Tang and Zhang [37], in this paper we present a more effective way to construct high-order symplectic integrators for... 
Hamiltonian systems | Legendre polynomial expansion | Continuous-stage Runge-Kutta-Nyström methods | Symplectic integrators | Simplifying assumptions | MATHEMATICS, APPLIED | CONSTRUCTION | FRAMEWORK | Continuous-stage Runge-Kutta-Nystrom methods
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 61, Issue 11, pp. 3381 - 3390
An explicit optimized Runge–Kutta–Nyström method with four stages and fifth algebraic order is developed. The produced method has variable coefficients with... 
Runge–Kutta–Nyström methods | Initial value problems | Phase-lag | Numerical solution | Explicit methods | Amplification factor | RungeKuttaNystrm methods | Runge-Kutta-Nystrom methods | MATHEMATICS, APPLIED
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2010, Volume 60, Issue 6, pp. 1639 - 1647
In this work we construct new Runge-Kutta-Nyström methods especially designed to integrate exactly the test equation y″=-w2y. We modify two existing methods:... 
Exponential fitting | Schrdinger equation | Runge-Kutta-Nyström methods
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 04/2014, Volume 30, pp. 56 - 60
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2014, Volume 260, pp. 482 - 493
The construction of symplectic methods of Runge–Kutta–Nyström type (RKN-type) specially adapted to the numerical solution of perturbed oscillators is analyzed.... 
Runge–Kutta–Nyström methods | Symplecticity | Perturbed oscillators | Second-order oscillatory Hamiltonian systems | Runge-Kutta-Nyström methods | Runge-Kutta-Nystrom methods | MATHEMATICS, APPLIED | NUMERICAL-INTEGRATION | Construction | Derivation | Truncation errors | Mathematical models | Runge-Kutta method | Standards | Oscillators | Optimization
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2019, Volume 363, p. 124634
Journal Article
Computer Physics Communications, ISSN 0010-4655, 12/2014, Volume 185, Issue 12, pp. 3151 - 3155
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 9, pp. 3517 - 3532
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2009, Volume 180, Issue 10, pp. 1777 - 1794
In this paper, extended Runge–Kutta–Nyström-type methods for the numerical integration of perturbed oscillators with low frequencies are presented, which... 
Extended tree theory | Order conditions | Perturbed oscillators | Runge–Kutta–Nyström-type methods | Runge-Kutta-Nyström-type methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Runge-Kutta-Nystrom-type methods | EXPLICIT ARKN METHODS | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | PAIR
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2019, Volume 353, pp. 204 - 209
Adapted Runge–Kutta–Nyström (ARKN) methods for solving the oscillatory problem q′′(t)+w2q(t)=f(q(t)) have been investigated by several authors. Recently, Shi... 
Hamiltonian systems | Oscillatory problems | Main frequency | Symplectic conditions | Adapted Runge–Kutta–Nyström methods | MATHEMATICS, APPLIED | Adapted Runge-Kutta-Nystrom methods | Information science | Methods
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 11/2019, Volume 145, pp. 469 - 487
Continuous-stage extended Runge-Kutta-Nyström (CSERKN) methods are proposed and developed for oscillatory problem q″(t)+Mq(t)=f(q(t)). These new methods take... 
Symmetric conditions | Extended Runge-Kutta-Nyström methods | Energy-preserving | Continuous stage method | Oscillatory Hamiltonian systems | MATHEMATICS, APPLIED | RKN METHODS | Extended Runge-Kutta-Nystrom methods | FALKNER-TYPE METHODS | FAMILY | HIGH-ORDER METHOD | CONSTRUCTION | NUMERICAL-INTEGRATION | EXPLICIT | Information science | Analysis | Methods
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 04/2016, Volume 71, Issue 7, pp. 1425 - 1447
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2009, Volume 180, Issue 10, pp. 1839 - 1846
A new Runge–Kutta–Nyström method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this... 
Runge–Kutta–Nyström methods | Phase-lag infinity | Phase-fitted | Initial-value problems | Runge-Kutta-Nyström methods | Runge-Kutta-Nystrom methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LAG | INTEGRATION | SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | NOUMEROV-TYPE METHOD
Journal Article
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