New methods for oscillatory problems based on classical codes
From MaRDI portal
Publication:1612454
DOI10.1016/S0168-9274(01)00147-7zbMath0998.65069MaRDI QIDQ1612454
Amelia García, Pablo Martín, Ana-Belén González
Publication date: 22 August 2002
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Nonlinear ordinary differential equations and systems (34A34) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05)
Related Items
Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations ⋮ A note on stability of multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems ⋮ A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems ⋮ On extended RKN integrators for multidimensional perturbed oscillators with applications ⋮ High order Runge--Kutta--Nyström codes for the integration of oscillatory problems. ⋮ A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators. ⋮ ERKN integrators for systems of oscillatory second-order differential equations ⋮ Multidimensional adapted Runge-Kutta-Nyström methods for oscillatory systems ⋮ Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation ⋮ A Runge-Kutta-Nyström pair for the numerical integration of perturbed oscillators ⋮ Stability and phase-lag analysis of explicit Runge-Kutta methods with variable coefficients for oscillatory problems ⋮ A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag ⋮ Order conditions for ARKN methods solving oscillatory systems ⋮ New \(4(3)\) pairs diagonally implicit Runge-Kutta-Nyström method for periodic IVPs ⋮ New methods for oscillatory systems based on ARKN methods ⋮ Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems ⋮ A \(5(3)\) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems ⋮ New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems ⋮ Diagonal implicit symplectic extended RKN methods for solving oscillatory Hamiltonian systems ⋮ Explicit multi-frequency symmetric extended RKN integrators for solving multi-frequency and multidimensional oscillatory reversible systems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Increased accuracy of computations in the main satellite problem through linearization methods
- Four-step exponential-fitted methods for nonlinear physical problems
- Improved numerical integration of perturbed oscillators via average
- Runge-Kutta(-Nyström) methods for ODEs with periodic solutions based on trigonometric polynomials
- An algorithm for the systematic construction of solutions to perturbed problems
- A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y=f(x,y)\)
- On the numerical integration of orbital problems with high-order Runge-Kutta-Nyström methods
- A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators
- Families of backward differentiation methods based on a new type of mixed interpolation
- Exponentially fitted Runge-Kutta methods
- Exponentially-fitted explicit Runge-Kutta methods
- Numerical calculation of the frequency of an oscillatory problem
- A four-stage implicit Runge-Kutta-Nyström method with variable coefficients for solving periodic initial value problems
- Numerical integration of ordinary differential equations based on trigonometric polynomials
- Numerical integration of products of Fourier and ordinary polynomials
- On numerical integration of perturbed linear oscillating systems
- Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
- Families of Runge-Kutta-Nystrom Formulae
- Multistep Numerical Methods Based on the Scheifele G-Functions with Application to Satellite Dynamics
- Solving Ordinary Differential Equations I
- High-Order Embedded Runge-Kutta-Nystrom Formulae
- A general canonical transformation increasing the number of variables with application to the two-body problem
- Exponential-fitted four-step methods for
- P-stability and exponential-fitting methods for y = f(x,y)