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Phase fitted algorithm for problems in quantum chemistry (Q2201016)

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scientific article

Language	Label	Description	Also known as
English	Phase fitted algorithm for problems in quantum chemistry	scientific article

Statements

scholarly article

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Phase fitted algorithm for problems in quantum chemistry (English)

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Marina A. Medvedeva

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Theodore E. Simos

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publication date

24 September 2020

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zbMATH Keywords

phase-lag

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derivative of the phase-lag

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initial value problems

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oscillating solution

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symmetric

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hybrid

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multistep

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Schrödinger equation

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describes a project that uses

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MaRDI profile type

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full work available at URL

https://doi.org/10.1007/s10910-020-01142-1

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

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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

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A four-stages multistep fraught in phase method for quantum chemistry problems

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

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A finite difference pair with improved phase and stability properties

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

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High-order P-stable multistep methods

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Stabilization of Cowell's method

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

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Unconditionally stable Noumerov-type methods for second order differential equations

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

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Numerov made explicit has better stability

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High-accuracy <i>P</i>-stable Methods for <i>y<sup>″</sup></i> = <i>f(t, y)</i>

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Chebyshevian multistep methods for ordinary differential equations

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Phase properties of high order, almost P-stable formulae

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Symmetric Multistip Methods for Periodic Initial Value Problems

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

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

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

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

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

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Non-dissipative extended one-step methods for oscillatory problems

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

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

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

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

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

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

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Coleman's method maximally adapted to the Schrödinger equation

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The Numerov method and singular potentials

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Numerov method maximally adapted to the Schrödinger equation

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

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Four-step exponential-fitted methods for nonlinear physical problems

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

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Exponential-fitted four-step methods for

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

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Numerical operations on oscillatory functions

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

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New three-stages symmetric two step method with improved properties for second order initial/boundary value problems

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An accomplished phase FD process for DEs in chemistry

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A phase fitted FinDiff process for DifEquns in quantum chemistry

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A multistage two-step fraught in phase scheme for problems in mathematical chemistry

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A Runge-Kutta type crowded in phase algorithm for quantum chemistry problems

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A multiple stage absolute in phase scheme for chemistry problems

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A perfect in phase FD algorithm for problems in quantum chemistry

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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

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

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Families of Runge-Kutta-Nystrom Formulae

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A family of embedded Runge-Kutta formulae

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Exponential Fitting method for the time-dependent Schrödinger equation

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

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

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

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

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

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A method for the solution of the Schrödinger equation

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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

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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

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

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

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

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

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

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

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New multiple stages two-step complete in phase algorithm with improved characteristics for second order initial/boundary value problems

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New four stages multistep in phase algorithm with best possible properties for second order problems

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Exponentially-fitted Obrechkoff methods for second-order differential equations

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

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

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

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

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

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

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

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

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

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

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

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

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Structure preservation of exponentially fitted Runge-Kutta methods

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

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Exponentially fitted symplectic integrators of RKN type for solving oscillatory problems

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New methods for oscillatory systems based on ARKN methods

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

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Stability of explicit ARKN methods for perturbed oscillators

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Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods

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

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

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

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

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

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

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

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

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Exponential fitted Gauss, Radau and Lobatto methods of low order

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

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

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

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

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

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A parallel ODE solver adapted to oscillatory problems

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

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

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

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

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

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

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

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Frequency evaluation for exponentially fitted Runge-Kutta methods

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Truncation Errors in Exponential Fitting for Oscillatory Problems

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Adapted BDF algorithms: Higher-order methods and their stability

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Exponential fitting BDF-Runge-Kutta algorithms

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

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

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

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Arbitrarily precise numerical solutions of the one-dimensional Schrödinger equation

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

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Journal of Mathematical Chemistry

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S10910-020-01142-1

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Sitelinks

Mathematics(1 entry)

mardi Publication:2201016

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