DOI10.1016/j.mcm.2005.09.015zbMath1086.65120OpenAlexW2002066913MaRDI QIDQ815422
Jesus Vigo Aguiar, Alicia Tocino
Publication date: 16 February 2006
Published in: Mathematical and Computer Modelling (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.mcm.2005.09.015
Symplectic and symmetric trigonometrically-fitted ARKN methods ⋮
Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations ⋮
A new finite difference method with optimal phase and stability properties for problems in chemistry ⋮
Efficient FinDiff algorithm with optimal phase properties for problems in quantum chemistry ⋮
New FD methods with phase-lag and its derivatives equal to zero for periodic initial value problems ⋮
A new method with vanished phase-lag and its derivatives of the highest order for problems in quantum chemistry ⋮
A new FinDiff numerical scheme with phase-lag and its derivatives equal to zero for periodic initial value problems ⋮
New FD scheme with vanished phase-lag and its derivatives up to order six for problems in chemistry ⋮
A new algorithm with eliminated phase-lag and its derivatives up to order five for problems in quantum chemistry ⋮
Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday ⋮
Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods ⋮
A multistep method with optimal phase and stability properties for problems in quantum chemistry ⋮
A multistep conditionally P-stable method with phase properties of high order for problems in quantum chemistry ⋮
Explicit symplectic RKN methods for perturbed non-autonomous oscillators: splitting, extended and exponentially fitting methods ⋮
A note on symplectic and symmetric ARKN methods ⋮
A phase-fitting and first derivative phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry ⋮
A phase-fitting, first and second derivatives phase-fitting singularly P-stable economical two-step method for problems in chemistry ⋮
A phase-fitting, first, second and third derivatives phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry ⋮
On the numerical stability of the exponentially fitted methods for first order IVPs ⋮
A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation ⋮
A phase fitted FiniteDiffr process for DiffrntEqutns in chemistry ⋮
A complete in phase FiniteDiffrnc algorithm for DiffrntEqutins in chemistry ⋮
Full in phase finite difference algorithm for differential equations in quantum chemistry ⋮
Limit-cycle-preserving simulation of gene regulatory oscillators ⋮
Solution of quantum chemical problems using an extremely successful and reasonably cost two-step, fourteenth-order phase-fitting approach ⋮
Solution of quantum chemical problems by a very effective and relatively inexpensive two-step, fourteenth-order, phase-fitting procedure ⋮
The existence of explicit symplectic ARKN methods with several stages and algebraic order greater than two ⋮
Phase-fitting, singularly P-stable, cost-effective two-step approach to solving problems in quantum chemistry with vanishing phase-lag derivatives up to order 6 ⋮
Two-step, fourteenth-order, phase-fitting procedure with high efficiency and minimal cost for chemical problems ⋮
Highly efficient, singularly P-stable, and low-cost phase-fitting two-step method of 14th order for problems in chemistry ⋮
Adapted Falkner-type methods solving oscillatory second-order differential equations ⋮
An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues ⋮
On symplectic and symmetric ARKN methods ⋮
Phase fitted algorithm for problems in quantum chemistry ⋮
A finite difference method with zero phase-lag and its derivatives for quantum chemistry problems ⋮
Complete in phase method for problems in chemistry ⋮
A finite difference method with phase-lag and its derivatives equal to zero for problems in chemistry ⋮
Symmetric and symplectic ERKN methods for oscillatory Hamiltonian systems ⋮
An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems ⋮
Solution to quantum chemistry problems using a phase-fitting, singularly P-stable, cost-effective two-step approach with disappearing phase-lag derivatives up to order 5 ⋮
Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems ⋮
A new family of phase-fitted and amplification-fitted Runge-Kutta type methods for oscillators ⋮
Trigonometrically fitted high-order predictor-corrector method with phase-lag of order infinity for the numerical solution of radial Schrödinger equation ⋮
Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs ⋮
A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation ⋮
Structure preservation of exponentially fitted Runge-Kutta methods ⋮
Symmetric and symplectic exponentially fitted Runge-Kutta-Nyström methods for Hamiltonian problems ⋮
Two-step method with vanished phase-lag and its derivatives for problems in quantum chemistry: an economical case ⋮
An economical two-step method with optimal phase and stability properties for problems in chemistry ⋮
A family of improved Falkner-type methods for oscillatory systems ⋮
Multiderivative extended Runge–Kutta–Nyström methods for multi-frequency oscillatory systems ⋮
A new eight-order symmetric two-step multiderivative method for the numerical solution of second-order IVPs with oscillating solutions ⋮
Runge-Kutta type methods with special properties for the numerical integration of ordinary differential equations ⋮
TWO NEW PHASE-FITTED SYMPLECTIC PARTITIONED RUNGE–KUTTA METHODS ⋮
A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method ⋮
Exponentially fitted singly diagonally implicit Runge-Kutta methods ⋮
Special extended Nyström tree theory for ERKN methods ⋮
Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods ⋮
Multi-step hybrid methods adapted to the numerical integration of oscillatory second-order systems ⋮
High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation ⋮
An accomplished phase FD process for DEs in chemistry ⋮
Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators ⋮
A new framework for solving partial differential equations using semi-analytical explicit RK(N)-type integrators ⋮
A new economical method with eliminated phase-lag and its derivative for problems in chemistry ⋮
Explicit almost P-stable Runge-Kutta-Nyström methods for the numerical solution of the two-body problem ⋮
A new method with improved phase-lag and stability properties for problems in quantum chemistry - an economical case ⋮
An economical two-step method with improved phase and stability properties for problems in chemistry ⋮
A new improved economical finite difference method for problems in quantum chemistry ⋮
An integrated in phase FD procedure for DiffEqns in chemical problems ⋮
A phase fitted FinDiff process for DifEquns in quantum chemistry ⋮
A complete in phase FinitDiff procedure for DiffEquns in chemistry ⋮
A phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry ⋮
A singularly P-stable two-step method with improved characteristics for problems in chemistry ⋮
Phase fitted method for quantum chemistry problems ⋮
A phase-fitting singularly P-stable cost-effective two-step method for solving chemistry problems ⋮
A perfect in phase FD algorithm for problems in quantum chemistry ⋮
The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods ⋮
Explicit multi-frequency symmetric extended RKN integrators for solving multi-frequency and multidimensional oscillatory reversible systems ⋮
An explicit trigonometrically fitted Runge–Kutta method for stiff and oscillatory problems with two frequencies ⋮
A two-step method singularly P-Stable with improved properties for problems in quantum chemistry ⋮
A two-step singularly P-Stable method with high phase and large stability properties for problems in chemistry