A new improved economical finite difference method for problems in quantum chemistry
type: Item
instance of: scholarly article
title: A new improved economical finite difference method for problems in quantum chemistry
zbMATH Open document ID: 1472.65085
author: Zheng Mingliang
author: T. E. Simos
publication date: 2021-08-17T00:00:00Z
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 7382639
zbMATH Keywords: phase-lag
zbMATH Keywords: derivative of the phase-lag
zbMATH Keywords: initial value problems
zbMATH Keywords: oscillating solution
zbMATH Keywords: hybrid method
zbMATH Keywords: multistep method
zbMATH Keywords: Schrödinger equation
describes a project that uses: EXPFIT4
describes a project that uses: LaTeX
MaRDI profile type: Publication
full work available at URL: s10910-021-01252-4
OpenAlex ID: W3168553284
cites work: The numerical solution of coupled differential equations arising from the Schrödinger equation
cites work: Q2353094
cites work: A new economical method with eliminated phase-lag and its derivative for problems in chemistry
cites work: A finite-difference method for the numerical solution of the Schrödinger equation
cites work: A new method with improved phase-lag and stability properties for problems in quantum chemistry - an economical case
cites work: A finite difference pair with improved phase and stability properties
cites work: Families of fifth order Nyström methods for y''=f(x,y) and intervals of periodicity
cites work: High-order P-stable multistep methods
cites work: Q4002473
cites work: Stabilization of Cowell's method
cites work: Intervals of periodicity and absolute stability of explicit Nyström methods for y''=f(x,y)
cites work: Unconditionally stable Noumerov-type methods for second order differential equations
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
cites work: Numerov made explicit has better stability
cites work: High-accuracy P-stable Methods for y″ = f(t, y)
cites work: Chebyshevian multistep methods for ordinary differential equations
cites work: Phase properties of high order, almost P-stable formulae
cites work: Symmetric Multistip Methods for Periodic Initial Value Problems
cites work: A new class of explicit two-step fourth order methods for \(y''=f(t,y)\) with extended intervals of periodicity
cites work: Families of two-step fourth order \(P\)-stable methods for second order differential equations
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
cites work: Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y''=f(t,y)\)
cites work: An explicit sixth-order method with phase-lag of order eight for \(y''=f(t,y)\)
cites work: Non-dissipative extended one-step methods for oscillatory problems
cites work: A two-stage fourth-order ``almost'' P-stable method for oscillatory problems
cites work: Singly-implicit stabilized extended one-step methods for second-order initial-value problems with oscillating solutions
cites work: Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
cites work: Analysis of a family of Chebyshev methods for \(y''=f(x,y)\)
cites work: P-stability and exponential-fitting methods for y'' = f(x,y)
cites work: Mixed collocation methods for \(y''=f(x,y)\)
cites work: Coleman's method maximally adapted to the Schrödinger equation
cites work: The Numerov method and singular potentials
cites work: Numerov method maximally adapted to the Schrödinger equation
cites work: EXPFIT4 -- a FORTRAN program for the numerical solution of systems of nonlinear second-order initial-value problems
cites work: Four-step exponential-fitted methods for nonlinear physical problems
cites work: Four step methods for \(y''=f(x,y)\)
cites work: Exponential-fitted four-step methods for
cites work: A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y''=f(x,y)\)
cites work: Numerical operations on oscillatory functions
cites work: Exponentially fitted variable two-step BDF algorithm for first order ODEs
cites work: A three-stages multistep teeming in phase algorithm for computational problems in chemistry
cites work: An accomplished phase FD process for DEs in chemistry
cites work: An integrated in phase FD procedure for DiffEqns in chemical problems
cites work: A phase fitted FinDiff process for DifEquns in quantum chemistry
cites work: A complete in phase FinitDiff procedure for DiffEquns in chemistry
cites work: A phase fitted FiniteDiffr process for DiffrntEqutns in chemistry
cites work: Full in phase finite difference algorithm for differential equations in quantum chemistry
cites work: 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
cites work: Comparison of some four-step methods for the numerical solution of the Schrödinger equation
cites work: Families of Runge-Kutta-Nystrom Formulae
cites work: A family of embedded Runge-Kutta formulae
cites work: Exponential Fitting method for the time-dependent Schrödinger equation
cites work: Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation
cites work: A variable step method for the numerical integration of the one- dimensional Schrödinger equation
cites work: Finite difference approach for the two-dimensional Schrödinger equation with application to scission-neutron emission
cites work: Weights of the exponential fitting multistep algorithms for first-order ODEs
cites work: Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
cites work: A method for the solution of the Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: 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

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cites work: Q3721711

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: 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

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: An economical eighth-order method for the approximation of the solution of the Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Two-step methods for the numerical solution of the Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Exponential-fitting methods for the numerical integration of the fourth-order differential equation \(y^{IV}+f\cdot y=g\)

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: On the generation of \(P\)-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods.

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: \(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: P-stable exponentially-fitted Obrechkoff methods of arbitrary order for second-order differential equations

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Exponentially-fitted Obrechkoff methods for second-order differential equations

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: The optimal exponentially-fitted Numerov method for solving two-point boundary value problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Two new embedded pairs of explicit Runge-Kutta methods adapted to the numerical solution of oscillatory problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Optimization of explicit two-step hybrid methods for solving orbital and oscillatory problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Symplectic explicit methods of Runge-Kutta-Nyström type for solving perturbed oscillators

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: On some new low storage implementations of time advancing Runge-Kutta methods

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Symmetric and symplectic exponentially fitted Runge-Kutta methods of high order

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: On high order symmetric and symplectic trigonometrically fitted Runge-Kutta methods with an even number of stages

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Accuracy and linear stability of RKN methods for solving second-order stiff problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Structure preservation of exponentially fitted Runge-Kutta methods

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta methods of Gauss type

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: New methods for oscillatory systems based on ARKN methods

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Stability of explicit ARKN methods for perturbed oscillators

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Q3561644

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A generator of families of two-step numerical methods with free parameters and minimal phase-lag

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: An explicit Numerov-type method for second-order differential equations with oscillating solutions

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: P-stable high-order super-implicit and Obrechkoff methods for periodic initial value problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Q3184858

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Exponential fitted Gauss, Radau and Lobatto methods of low order

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A new two-step hybrid method for the numerical solution of the Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: \(P\)-stable higher derivative methods with minimal phase-lag for solving second order differential equations

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: An improved trigonometrically fitted P-stable Obrechkoff method for periodic initial-value problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Properties and implementation of \(r\)-Adams methods based on mixed-type interpolation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A parallel ODE solver adapted to oscillatory problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Trigonometrically-fitted method with the Fourier frequency spectrum for undamped Duffing equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Trigonometrically-fitted method for a periodic initial value problem with two frequencies

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations.

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A parallel boundary value technique for singularly perturbed two-point boundary value problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: The various order explicit multistep exponential fitting for systems of ordinary differential equations

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: The arbitrary order implicit multistep schemes of exponential fitting and their applications

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Frequency evaluation for exponentially fitted Runge-Kutta methods

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Truncation Errors in Exponential Fitting for Oscillatory Problems

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Adapted BDF algorithms: Higher-order methods and their stability

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Exponential fitting BDF-Runge-Kutta algorithms

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Obrechkoff one-step method fitted with Fourier spectrum for undamped Duffing equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A P-STABLE EIGHTEENTH-ORDER SIX-STEP METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (cites work)
cites work: A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation

A new improved economical finite difference method for problems in quantum chemistry (DOI)
DOI: 10.1007/S10910-021-01252-4

A new improved economical finite difference method for problems in quantum chemistry (published in)
published in: Journal of Mathematical Chemistry