DOI10.1098/rspa.2003.1210zbMath1041.65058OpenAlexW2081801878MaRDI QIDQ3043451
José Manuel Ferrándiz, Theodore E. Simos, Jesus Vigo Aguiar
Publication date: 6 August 2004
Published in: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1098/rspa.2003.1210
Symplectic and symmetric trigonometrically-fitted ARKN methods,
Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations,
A trigonometrically-fitted method with two frequencies, one for the solution and another one for the derivative,
An adapted explicit hybrid four-step method for the numerical solution of perturbed oscillators,
Multi-step hybrid methods for special second-order differential equations \(y^{\prime \prime}(t)=f(t,y(t))\),
New explicit adapted Numerov methods for second-order oscillatory differential equations,
Limit-cycle-preserving simulation of gene regulatory oscillators,
New optimized explicit modified RKN methods for the numerical solution of the Schrödinger equation,
Two-step extended RKN methods for oscillatory systems,
A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models,
Adapted Falkner-type methods solving oscillatory second-order differential equations,
A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation,
Symplectic exponentially-fitted four-stage Runge-Kutta methods of the Gauss type,
Exponentially-fitted methods and their stability functions,
A new family of phase-fitted and amplification-fitted Runge-Kutta type methods for oscillators,
New optimized two-derivative Runge-Kutta type methods for solving the radial Schrödinger equation,
A 6(4) optimized embedded Runge-Kutta-Nyström pair for the numerical solution of periodic problems,
A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation,
Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations,
A family of improved Falkner-type methods for oscillatory systems,
Exponentially fitted TDRK pairs for the Schrödinger equation,
Revised trigonometrically fitted two-step hybrid methods with equation dependent coefficients for highly oscillatory problems,
Runge-Kutta-Nyström methods with equation dependent coefficients and reduced phase lag for oscillatory problems,
Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\),
THDRK methods with vanished phase-lag and its first derivative for the Schrödinger equation,
ERKN integrators for systems of oscillatory second-order differential equations,
Analytical approximate solutions for conservative nonlinear oscillators by modified rational harmonic balance method,
Exponential fitting BDF-Runge-Kutta algorithms,
Extended RKN-type methods for numerical integration of perturbed oscillators,
Energy-preserving continuous stage extended Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems,
Symmetric trigonometrically-fitted two-step hybrid methods for oscillatory problems,
Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives,
Scheifele two-step methods for perturbed oscillators,
Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations,
New optimized symmetric and symplectic trigonometrically fitted RKN methods for second-order oscillatory differential equations,
Frequency evaluation for exponentially fitted Runge-Kutta methods,
The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods,
Trigonometrically fitted multi-step hybrid methods for oscillatory special second-order initial value problems,
Explicit multi-frequency symmetric extended RKN integrators for solving multi-frequency and multidimensional oscillatory reversible systems