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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
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 03/2015, Volume 20, Issue 3, pp. 650 - 667
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, 2011, Volume 62, Issue 4, pp. 2101 - 2111
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... 
Mathematica | Integer partitions | Initial value problems | Runge–Kutta methods | Rooted trees | Truncation error | RungeKutta methods | MATHEMATICS, APPLIED | Runge-Kutta methods | PAIRS | Trees | Theorems | Algebra | Enumeration | Perturbation methods | Mathematical analysis | Mathematical models | Runge-Kutta method
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2014, Volume 83, Issue 288, pp. 1689 - 1700
No Runge-Kutta method can be energy preserving for all Hamiltonian systems. But for problems in which the Hamiltonian is a polynomial, the averaged vector... 
Astronomical quadratures | Inner products | Quadratic polynomials | Vector fields | Sunlight | Polynomials | Runge Kutta method | Gaussian quadratures | Degrees of polynomials | Vertices | Polynomial Hamiltonian systems | Energy preservation | Runge-Kutta methods | MATHEMATICS, APPLIED | polynomial Hamiltonian systems | SERIES | INTEGRATORS
Journal Article
Fuzzy Sets and Systems, ISSN 0165-0114, 01/2018, Volume 331, pp. 47 - 67
In this paper, an extended fourth-order Runge–Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a... 
Characterization theorem | Fuzzy ordinary differential equations | Fuzzy differentiability | Error analysis | Runge–Kutta methods | EXISTENCE | INTERVAL | MATHEMATICS, APPLIED | CALCULUS | CAUCHY-PROBLEM | STATISTICS & PROBABILITY | INTEGRATION | COMPUTER SCIENCE, THEORY & METHODS | Runge-Kutta methods | VALUED FUNCTIONS
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 4, pp. 1056 - 1070
Journal Article
Applied Mathematics and Information Sciences, ISSN 1935-0090, 2013, Volume 7, Issue 2, pp. 433 - 437
Journal Article
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
Computers and Mathematics with Applications, ISSN 0898-1221, 06/2018, Volume 75, Issue 12, pp. 4505 - 4533
The third paper in our series on open source MATLAB/GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation.... 
GNU Octave | Open source | Hybridized discontinuous Galerkin (HDG) method | MATLAB | Vectorization | Diagonally implicit Runge–Kutta method (DIRK) | Rapid prototyping | Methods | Mathematics - Numerical Analysis
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 200 - 220
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
Applied Mathematics and Computation, ISSN 0096-3003, 12/2019, Volume 363, p. 124634
Journal Article
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 03/2019, Volume 345, pp. 502 - 517
Journal Article