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Numerical Algorithms, ISSN 1017-1398, 11/2018, Volume 79, Issue 3, pp. 787 - 800
Two derivative Runge-Kutta methods are Runge-Kutta methods for problems of the form y ′ = f(y) that include the second derivative y ″ = g(y) = f ′(y)f(y) and... 
Two derivative Runge-Kutta methods | Algorithms | Algebra | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Trigonometrical fitting | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | 2-STEP HYBRID METHODS | STABILITY | International trade | Information science | Analysis | 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
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2018, Volume 344, pp. 115 - 131
In this paper, we propose a general class of trigonometrically-fitted two-step hybrid (TFTSH) methods for solving numerically oscillatory second-order initial... 
Oscillatory problems | Order conditions | Two-step hybrid methods | Generalized B2-series | Trigonometrical-fitting | Symmetry | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | COLLOCATION METHODS | ORDER | NUMERICAL-INTEGRATION | SYSTEMS | Y | PERTURBED OSCILLATORS | Information science
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 12/2016, Volume 1790, Issue 1
In this work we consider trigonometrically fitted two step hybrid methods for the numerical solution of second-order initial value problems. We follow the... 
trigonometrical fitting | oscillatory problems | Two Step Hybrid methods | Boundary value problems | Numerical methods | Numerical integration
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2019, Volume 42, Issue 6, pp. 1955 - 1966
Two‐derivative Runge‐Kutta methods are Runge‐Kutta methods for problems of the form y′ = f(y) that include the second derivative y′′ = g(y) = f ′(y)f(y) and... 
periodic or oscillatory behavior | trigonometrical fitting | two‐derivative Runge‐Kutta methods | two-derivative Runge-Kutta methods | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | INTEGRATION | STABILITY | INITIAL-VALUE PROBLEMS | Coefficients | Test procedures | Construction methods
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 09/2017, Volume 74, Issue 5, pp. 1029 - 1042
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 08/2019, Volume 142, pp. 171 - 189
A new family of modified two-derivative Runge-Kutta-Nyström (TDRKN) methods are proposed for solving initial value problems of second-order oscillatory... 
Two-derivative Runge-Kutta-Nyström method | Nyström tree | Order condition | Periodicity region | B-series | Trigonometrical fitting | Two-derivative Runge-Kutta-Nystrom method | MATHEMATICS, APPLIED | Nystrom tree | SYSTEMS | Analysis | Methods | Differential equations
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 03/2018, Volume 320, pp. 740 - 753
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 05/2017, Volume 94, Issue 5, pp. 1036 - 1061
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 06/2016, Volume 1738, Issue 1
The purpose of the talk is the presentation of some recent advances in the numerical solution of differential equations, with special emphasis to... 
trigonometrical fitting | Numerical methods | partial differential equations | Solvers | Ordinary differential equations | Method of lines | Qualitative analysis | Differential equations
Journal Article
APPLIED MATHEMATICS LETTERS, ISSN 0893-9659, 05/2004, Volume 17, Issue 5, pp. 601 - 607
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2007, Volume 189, Issue 1, pp. 178 - 185
In this paper we present a kind of trigonometrically fitted explicit two-step hybrid method which achieves algebraic order six. The new method is zero... 
Two-step hybrid method | Orbital problems | Trigonometrical-fitting | MATHEMATICS, APPLIED | trigonometrical-fitting | RUNGE-KUTTA METHODS | MULTISTEP METHODS | INITIAL-VALUE-PROBLEMS | NYSTROM METHODS | orbital problems | two-step hybrid method | OSCILLATING SOLUTIONS
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 02/2020, Volume 97, Issue 1-2, pp. 85 - 94
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2014, Volume 232, pp. 643 - 657
Journal Article
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