A low-cost, two-step fourteenth-order phase-fitting approach to tackling problems in chemistry

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Cites Work

Families of Runge-Kutta-Nystrom Formulae
A P-STABLE EIGHTEENTH-ORDER SIX-STEP METHOD FOR PERIODIC INITIAL VALUE PROBLEMS
High-accuracy P-stable Methods for y^″ = f(t, y)
Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
Symmetric Multistip Methods for Periodic Initial Value Problems
Non-dissipative extended one-step methods for oscillatory problems
A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems
Exponential-fitted four-step methods for
Numerical operations on oscillatory functions
P-stability and exponential-fitting methods for y = f(x,y)
An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems
A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS
Truncation Errors in Exponential Fitting for Oscillatory Problems
The Numerov method and singular potentials
Mixed collocation methods for \(y=f(x,y)\)
A parallel ODE solver adapted to oscillatory problems
Weights of the exponential fitting multistep algorithms for first-order ODEs
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
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
An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues
Note on derivation of order conditions for ARKN methods for perturbed oscillators
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A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation
Two new embedded pairs of explicit Runge-Kutta methods adapted to the numerical solution of oscillatory problems
\(P\)-stable higher derivative methods with minimal phase-lag for solving second order differential equations
On some new low storage implementations of time advancing Runge-Kutta methods
A low computational cost eight algebraic order hybrid method with vanished phase-lag and its first, second, third and fourth derivatives for the approximate solution of the Schrödinger equation
Optimization of explicit two-step hybrid methods for solving orbital and oscillatory problems
Symmetric and symplectic exponentially fitted Runge-Kutta methods of high order
A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation
Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation
A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation
Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs
Four step methods for \(y=f(x,y)\)
The arbitrary order implicit multistep schemes of exponential fitting and their applications
A parallel boundary value technique for singularly perturbed two-point boundary value problems
Exponentially fitted variable two-step BDF algorithm for first order ODEs
Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation
Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation
Obrechkoff one-step method fitted with Fourier spectrum for undamped Duffing equation
Trigonometrically-fitted method for a periodic initial value problem with two frequencies
Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems
Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta methods of Gauss type
Exponential fitting BDF-Runge-Kutta algorithms
Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission
Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type
Exponential-fitting methods for the numerical integration of the fourth-order differential equation \(y^{IV}+f\cdot y=g\)
High-order P-stable multistep methods
Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
On the generation of \(P\)-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods.
A new two-step hybrid method for the numerical solution of the Schrödinger equation
A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation
Structure preservation of exponentially fitted Runge-Kutta methods
Exponential fitted Gauss, Radau and Lobatto methods of low order
Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type
Exponentially-fitted Obrechkoff methods for second-order differential equations
Accuracy and linear stability of RKN methods for solving second-order stiff problems
The optimal exponentially-fitted Numerov method for solving two-point boundary value problems
Unconditionally stable Noumerov-type methods for second order differential equations
A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
Numerov made explicit has better stability
Phase properties of high order, almost P-stable formulae
A variable step method for the numerical integration of the one- dimensional Schrödinger equation
A new class of explicit two-step fourth order methods for \(y=f(t,y)\) with extended intervals of periodicity
Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y=f(t,y)\)
A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
Families of two-step fourth order \(P\)-stable methods for second order differential equations
Numerov method maximally adapted to the Schrödinger equation
Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
A method for the solution of the Schrödinger equation
Coleman's method maximally adapted to the Schrödinger equation
Families of fifth order Nyström methods for y=f(x,y) and intervals of periodicity
A family of embedded Runge-Kutta formulae
Intervals of periodicity and absolute stability of explicit Nyström methods for y=f(x,y)
Two-step methods for the numerical solution of the Schrödinger equation
Analysis of a family of Chebyshev methods for \(y=f(x,y)\)
Four-step exponential-fitted methods for nonlinear physical problems
EXPFIT4 -- a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems
A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y=f(x,y)\)
A finite-difference method for the numerical solution of the Schrödinger equation
A two-stage fourth-order ``almost P-stable method for oscillatory problems
Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.
Singly-implicit stabilized extended one-step methods for second-order initial-value problems with oscillating solutions
Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs
An efficient and economical high order method for the numerical approximation of the Schrödinger equation
A generator of families of two-step numerical methods with free parameters and minimal phase-lag
A finite difference pair with improved phase and stability properties
Stability of explicit ARKN methods for perturbed oscillators
An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
Comparison of some four-step methods for the numerical solution of the Schrödinger equation
Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators
The various order explicit multistep exponential fitting for systems of ordinary differential equations
Properties and implementation of \(r\)-Adams methods based on mixed-type interpolation
Exponential Fitting method for the time-dependent Schrödinger equation
Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation
A three-stages multistep teeming in phase algorithm for computational problems in chemistry
A phase-fitting singularly P-stable cost-effective two-step method for solving chemistry problems
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
A complete in phase FiniteDiffrnc algorithm for DiffrntEqutins in chemistry
A Runge-Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equation
An economical eighth-order method for the approximation of the solution of the Schrödinger equation
An explicit Numerov-type method for second-order differential equations with oscillating solutions
Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday
On high order symmetric and symplectic trigonometrically fitted Runge-Kutta methods with an even number of stages
A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems
Adapted BDF algorithms: Higher-order methods and their stability
An efficient and computational effective method for second order problems
P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems
P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations
Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)
A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions
New methods for oscillatory systems based on ARKN methods
Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators
The numerical solution of coupled differential equations arising from the Schrödinger equation
Stabilization of Cowell's method
Chebyshevian multistep methods for ordinary differential equations
Frequency evaluation for exponentially fitted Runge-Kutta methods
\(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations
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
Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)

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