A multistep method with optimal properties for second order differential equations (Q1703391)

scientific article; zbMATH DE number 6846162

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English	A multistep method with optimal properties for second order differential equations	scientific article; zbMATH DE number 6846162

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instance of

scholarly article

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title

A multistep method with optimal properties for second order differential equations (English)

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2 March 2018

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zbMATH Keywords

Schrödinger equation

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multistep methods

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multistage methods

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interval of periodicity

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phase-lag

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phase-fitted

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derivatives of the phase-lag

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finite difference method

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numerical example

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local truncation error

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algorithm

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stability

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computational efficiency

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describes a project that uses

LaTeX

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Publication

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full work available at URL

https://doi.org/10.1007/s10910-017-0774-4

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cites work

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The use of phase lag and amplification error derivatives for the construction of a modified Runge-Kutta-Nyström method

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Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems

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Runge-Kutta type methods with special properties for the numerical integration of ordinary differential equations

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A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation

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Efficient low computational cost hybrid explicit four-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the Schrödinger equation

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Family of symmetric linear six-step methods with vanished phase-lag and its derivatives and their application to the radial Schrödinger equation and related problems

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A family of two stages tenth algebraic order symmetric six-step methods with vanished phase-lag and its first derivatives for the numerical solution of the radial Schrödinger equation and related problems

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A new two stages tenth algebraic order symmetric six-step method with vanished phase-lag and its first and second derivatives for the solution of the radial Schrödinger equation and related problems

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New two stages high order symmetric six-step method with vanished phase-lag and its first, second and third derivatives for the numerical solution of the Schrödinger equation

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A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problems

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New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. I: construction and theoretical analysis

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An explicit four-step method with vanished phase-lag and its first and second derivatives

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An explicit linear six-step method with vanished phase-lag and its first derivative

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A new explicit hybrid four-step method with vanished phase-lag and its derivatives

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A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrödinger equation

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A family of embedded explicit six-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation: development and theoretical analysis

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A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equation

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An implicit symmetric linear six-step methods with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation and related problems

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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 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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A new eight algebraic order embedded explicit six-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation

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A new explicit four-step method with vanished phase-lag and its first and second derivatives

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Symplectic methods for the numerical solution of the radial Schrödinger equation

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Closed Newton-Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equation

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CLOSED NEWTON–COTES TRIGONOMETRICALLY-FITTED FORMULAE FOR LONG-TIME INTEGRATION

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High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation

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TWO NEW PHASE-FITTED SYMPLECTIC PARTITIONED RUNGE–KUTTA METHODS

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Three stages symmetric six-step method with eliminated phase-lag and its derivatives for the solution of the Schrödinger equation

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High order computationally economical six-step method with vanished phase-lag and its derivatives 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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published in

Journal of Mathematical Chemistry

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Identifiers

zbMATH Open document ID

1384.65049

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Mathematics Subject Classification ID

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10.1007/S10910-017-0774-4

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Sitelinks

Mathematics(1 entry)

mardi Publication:1703391