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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 Numerical Mathematics, ISSN 0168-9274, 05/2017, Volume 115, pp. 1 - 15
In this paper we introduce a family of stochastic Runge–Kutta Rosenbrock (SRKR) type methods for multi-dimensional Itô stochastic differential equations... 
Stochastic B-series | Stochastic differential equations | Computational effort | Stochastic Runge–Kutta Rosenbrock type methods | Stochastic Runge-Kutta Rosenbrock type | MATHEMATICS, APPLIED | TAYLOR EXPANSIONS | WEAK APPROXIMATION | methods | ROOTED TREE ANALYSIS | ORDER CONDITIONS | FUNCTIONALS | Analysis | Methods | Differential equations
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 200 - 220
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2019, Volume 42, Issue 18, pp. 7349 - 7358
The classical four‐stage family of explicit sixth‐order Numerov‐type method is considered. We provide two kinds of interpolants: (a) a three‐step interpolation... 
y″=f(x,y) | explicit hybrid Numerov | interpolation | PREDICTOR-CORRECTOR METHOD | MATHEMATICS, APPLIED | HYBRID 4-STEP METHODS | y ''=f(x | SCHRODINGER-EQUATION | 2-STEP METHODS | HIGH-ORDER | VANISHED PHASE-LAG | NUMERICAL-SOLUTION | EFFICIENT INTEGRATION | y | RUNGE-KUTTA PAIRS | P-STABLE METHOD | Interpolation | Mathematical analysis
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2014, Volume 234, pp. 179 - 191
Journal Article
Physics Reports, ISSN 0370-1573, 03/2014, Volume 536, Issue 3, pp. 75 - 146
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 | KUTTA-NYSTROM METHODS | SYSTEMS | EXPLICIT ARKN METHODS | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | PAIR
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2018, Volume 15, Issue 2, pp. 1 - 17
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 02/2020, Volume 43, Issue 3, pp. 1204 - 1215
The explicit sixth‐order Numerov‐type family of methods is considered. A new representative from this family is produced and equipped with a cheap step‐size... 
variable step | y″ = f (x, y) | explicit hybrid Numerov | MATHEMATICS, APPLIED | SOLVING Y | HIGH-ORDER | VANISHED PHASE-LAG | y '' = f (x | 6TH ORDER | SYMBOLIC DERIVATION | RUNGE-KUTTA PAIRS | P-STABLE METHOD | 4-STEP METHODS | 2-STEP HYBRID METHODS | NOUMEROV-TYPE METHOD | Algorithms
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 03/2020, Volume 404, p. 109105
Journal Article