A new improved economical finite difference method for problems in quantum chemistry (Q2046283)

scientific article; zbMATH DE number 7382639

Language	Label	Description	Also known as
English	A new improved economical finite difference method for problems in quantum chemistry	scientific article; zbMATH DE number 7382639

Statements

instance of

scholarly article

0 references

title

A new improved economical finite difference method for problems in quantum chemistry (English)

0 references

0 references

0 references

17 August 2021

0 references

zbMATH Keywords

phase-lag

0 references

derivative of the phase-lag

0 references

initial value problems

0 references

oscillating solution

0 references

hybrid method

0 references

multistep method

0 references

Schrödinger equation

0 references

describes a project that uses

0 references

0 references

0 references

full work available at URL

https://doi.org/10.1007/s10910-021-01252-4

0 references

cites work

The numerical solution of coupled differential equations arising from the Schrödinger equation

0 references

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

0 references

A new economical method with eliminated phase-lag and its derivative for problems in chemistry

0 references

A finite-difference method for the numerical solution of the Schrödinger equation

0 references

A new method with improved phase-lag and stability properties for problems in quantum chemistry - an economical case

0 references

A finite difference pair with improved phase and stability properties

0 references

Families of fifth order Nyström methods for y''=f(x,y) and intervals of periodicity

0 references

High-order P-stable multistep methods

0 references

Q4002473

0 references

Stabilization of Cowell's method

0 references

Intervals of periodicity and absolute stability of explicit Nyström methods for y''=f(x,y)

0 references

Unconditionally stable Noumerov-type methods for second order differential equations

0 references

A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems

0 references

Numerov made explicit has better stability

0 references

High-accuracy P-stable Methods for y″ = f(t, y)

0 references

Chebyshevian multistep methods for ordinary differential equations

0 references

Phase properties of high order, almost P-stable formulae

0 references

Symmetric Multistip Methods for Periodic Initial Value Problems

0 references

A new class of explicit two-step fourth order methods for \(y''=f(t,y)\) with extended intervals of periodicity

0 references

Families of two-step fourth order \(P\)-stable methods for second order differential equations

0 references

A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method

0 references

Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y''=f(t,y)\)

0 references

An explicit sixth-order method with phase-lag of order eight for \(y''=f(t,y)\)

0 references

Non-dissipative extended one-step methods for oscillatory problems

0 references

A two-stage fourth-order ``almost'' P-stable method for oscillatory problems

0 references

Singly-implicit stabilized extended one-step methods for second-order initial-value problems with oscillating solutions

0 references

Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine

0 references

Analysis of a family of Chebyshev methods for \(y''=f(x,y)\)

0 references

P-stability and exponential-fitting methods for y'' = f(x,y)

0 references

Mixed collocation methods for \(y''=f(x,y)\)

0 references

Coleman's method maximally adapted to the Schrödinger equation

0 references

The Numerov method and singular potentials

0 references

Numerov method maximally adapted to the Schrödinger equation

0 references

EXPFIT4 -- a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems

0 references

Four-step exponential-fitted methods for nonlinear physical problems

0 references

Four step methods for \(y''=f(x,y)\)

0 references

Exponential-fitted four-step methods for

0 references

A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y''=f(x,y)\)

0 references

Numerical operations on oscillatory functions

0 references

Exponentially fitted variable two-step BDF algorithm for first order ODEs

0 references

A three-stages multistep teeming in phase algorithm for computational problems in chemistry

0 references

An accomplished phase FD process for DEs in chemistry

0 references

An integrated in phase FD procedure for DiffEqns in chemical problems

0 references

A phase fitted FinDiff process for DifEquns in quantum chemistry

0 references

A complete in phase FinitDiff procedure for DiffEquns in chemistry

0 references

A phase fitted FiniteDiffr process for DiffrntEqutns in chemistry

0 references

Full in phase finite difference algorithm for differential equations in quantum chemistry

0 references

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

0 references

Comparison of some four-step methods for the numerical solution of the Schrödinger equation

0 references

Families of Runge-Kutta-Nystrom Formulae

0 references

A family of embedded Runge-Kutta formulae

0 references

Exponential Fitting method for the time-dependent Schrödinger equation

0 references

Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation

0 references

A variable step method for the numerical integration of the one- dimensional Schrödinger equation

0 references

Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission

0 references

Weights of the exponential fitting multistep algorithms for first-order ODEs

0 references

Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation

0 references

A method for the solution of the Schrödinger equation

0 references

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

0 references

Q3721711

0 references

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

0 references

An economical eighth-order method for the approximation of the solution of the Schrödinger equation

0 references

Two-step methods for the numerical solution of the Schrödinger equation

0 references

Exponential-fitting methods for the numerical integration of the fourth-order differential equation \(y^{IV}+f\cdot y=g\)

0 references

On the generation of \(P\)-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods.

0 references

\(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations

0 references

P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations

0 references

A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions

0 references

Exponentially-fitted Obrechkoff methods for second-order differential equations

0 references

The optimal exponentially-fitted Numerov method for solving two-point boundary value problems

0 references

Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs

0 references

Two new embedded pairs of explicit Runge-Kutta methods adapted to the numerical solution of oscillatory problems

0 references

Optimization of explicit two-step hybrid methods for solving orbital and oscillatory problems

0 references

Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs

0 references

Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators

0 references

Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type

0 references

On some new low storage implementations of time advancing Runge-Kutta methods

0 references

Symmetric and symplectic exponentially fitted Runge-Kutta methods of high order

0 references

On high order symmetric and symplectic trigonometrically fitted Runge-Kutta methods with an even number of stages

0 references

Accuracy and linear stability of RKN methods for solving second-order stiff problems

0 references

Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type

0 references

Structure preservation of exponentially fitted Runge-Kutta methods

0 references

Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta methods of Gauss type

0 references

Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems

0 references

New methods for oscillatory systems based on ARKN methods

0 references

Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators

0 references

Stability of explicit ARKN methods for perturbed oscillators

0 references

Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods

0 references

Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)

0 references

Q3561644

0 references

A generator of families of two-step numerical methods with free parameters and minimal phase-lag

0 references

A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation

0 references

A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS

0 references

An explicit Numerov-type method for second-order differential equations with oscillating solutions

0 references

A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems

0 references

P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems

0 references

Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)

0 references

Q3184858

0 references

Exponential fitted Gauss, Radau and Lobatto methods of low order

0 references

A new two-step hybrid method for the numerical solution of the Schrödinger equation

0 references

\(P\)-stable higher derivative methods with minimal phase-lag for solving second order differential equations

0 references

Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation

0 references

An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems

0 references

Properties and implementation of \(r\)-Adams methods based on mixed-type interpolation

0 references

A parallel ODE solver adapted to oscillatory problems

0 references

Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation

0 references

Trigonometrically-fitted method for a periodic initial value problem with two frequencies

0 references

A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems

0 references

Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.

0 references

A parallel boundary value technique for singularly perturbed two-point boundary value problems

0 references

The various order explicit multistep exponential fitting for systems of ordinary differential equations

0 references

The arbitrary order implicit multistep schemes of exponential fitting and their applications

0 references

Frequency evaluation for exponentially fitted Runge-Kutta methods

0 references

Truncation Errors in Exponential Fitting for Oscillatory Problems

0 references

Adapted BDF algorithms: Higher-order methods and their stability

0 references

Exponential fitting BDF-Runge-Kutta algorithms

0 references

Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday

0 references

Obrechkoff one-step method fitted with Fourier spectrum for undamped Duffing equation

0 references

A P-STABLE EIGHTEENTH-ORDER SIX-STEP METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

0 references

Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation

0 references

A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation

0 references

published in

Journal of Mathematical Chemistry

0 references

Identifiers

zbMATH Open document ID

1472.65085

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

10.1007/S10910-021-01252-4

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:2046283