A 6(4) optimized embedded Runge-Kutta-Nyström pair for the numerical solution of periodic problems
From MaRDI portal
Publication:457741
DOI10.1016/j.cam.2014.07.016zbMath1337.65066OpenAlexW2015025253MaRDI QIDQ457741
A. A. Kosti, Zacharias A. Anastassi
Publication date: 29 September 2014
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2014.07.016
initial value problemsRunge-Kutta-Nyström methodsnumerical solutionembedded pairsphase fittingamplification fitting
Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)
Related Items
A trigonometrically fitted block method for solving oscillatory second-order initial value problems and Hamiltonian systems, A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems, A phase- and amplification-fitted 5(4) diagonally implicit Runge-Kutta-Nyström pair for oscillatory systems, A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems, Editorial: Recent trends on computational and mathematical methods in science and engineering (CMMSE), Unnamed Item, A cycle-based formulation for the simulation of multi time-scale systems -- application to the modeling of the storage system of a fully electric ferry, A new fourth-order four stage explicit trigonometrically-fitted Runge–Kutta–Nyström method for solving periodic problems, Adaptive multi-step Runge-Kutta-Nyström methods for general second-order ordinary differential equations
Cites Work
- A trigonometrically-fitted method with two frequencies, one for the solution and another one for the derivative
- A strategy for selecting the frequency in trigonometrically-fitted methods based on the minimization of the local truncation errors and the total energy error
- Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
- A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
- High-order P-stable multistep methods
- Stability of collocation-based Runge-Kutta-Nyström methods
- Stability of Runge-Kutta-Nyström methods
- On the frequency choice in trigonometrically fitted methods
- A \(5(3)\) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems
- Unconditionally stable methods for second order differential equations
- Compuation of the interval of stability of Runge-Kutta-Nyström methods
- A new optimized non-FSAL embedded Runge-Kutta-Nyström algorithm of orders 6 and 4 in six stages
- New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation
- An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems
- Exponentially fitted singly diagonally implicit Runge-Kutta methods
- New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems
- Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
- Stabilization of Cowell's method
- A NEW SYMMETRIC EIGHT-STEP PREDICTOR-CORRECTOR METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION AND RELATED ORBITAL PROBLEMS
- Families of Runge-Kutta-Nystrom Formulae
- Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
- Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
- Four-stage symplectic and P-stable SDIRKN methods with dispersion of high order
- An exponentially-fitted high order method for long-term integration of periodic initial-value problems
