A new multistep finite difference pair for the Schrödinger equation and related problems (Q1742794)

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scientific article; zbMATH DE number 6858960

Language	Label	Description	Also known as
English	A new multistep finite difference pair for the Schrödinger equation and related problems	scientific article; zbMATH DE number 6858960

Statements

scholarly article

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A new multistep finite difference pair for the Schrödinger equation and related problems (English)

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Dmitriy B. Berg

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publication date

12 April 2018

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The authors announce a new three-stages symmetric six-step finite difference pair. The numerical experiments obtained by the new developed finite difference pair and the well-known and recently produced pairs to the radial Schrödinger equation are presented. The main contribution of the paper consists of a comparative study of the new finite difference pair with other finite difference pairs of the same family.

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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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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/s10910-017-0812-2

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An efficient six-step method for the solution of the Schrödinger equation

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Special issue: The international conference on computational methods in sciences and engineering 2004 (ICCMSE-2004), Vouliagmeni, Greece, November 19--23, 2004. Selected papers based on the presentation at the conference.

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Special Issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE 2003), Kastoria, Greece, September 12--16, 2003.

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

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A high-order two-step phase-fitted method for the numerical solution of the Schrödinger equation

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A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation

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A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation

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Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics

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An optimized Runge-Kutta method for the solution of orbital problems

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A NEW METHODOLOGY FOR THE CONSTRUCTION OF OPTIMIZED RUNGE–KUTTA–NYSTRÖM METHODS

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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 exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods

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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 order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method

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An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems

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Construction of trigonometrically and exponentially fitted Runge--Kutta--Nyström methods for the numerical solution of the Schrödinger equation and related problems -- a method of 8th algebraic order

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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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Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions

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Optimized Runge-Kutta pairs for problems with oscillating solutions

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Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation

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A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation

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Symmetric Multistip Methods for Periodic Initial Value Problems

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An optimized two-step hybrid block method for solving general second order initial-value problems

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On modified Runge-Kutta trees and methods

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Phase-fitted Runge-Kutta pairs of orders 8(7)

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Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs

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Families of Runge-Kutta-Nystrom Formulae

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A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. I: Development of the basic method

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

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

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A generator and an optimized generator of high-order hybrid explicit methods for the numerical solution of the Schrödinger equation. II: Development of the generator, optimization of the generator and numerical results

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Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation

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A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation

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Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions

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Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation

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A family of multiderivative methods for the numerical solution of the Schrödinger equation

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

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

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A new Numerov-type method for the numerical solution of the Schrödinger equation

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A NEW SYMMETRIC EIGHT-STEP PREDICTOR-CORRECTOR METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION AND RELATED ORBITAL PROBLEMS

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A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutions

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Optimizing a hybrid two-step method for the numerical solution of the Schrödinger equation and related problems with respect to phase-lag

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A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation

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A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation

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A new four-step hybrid type method with vanished phase-lag and its first derivatives for each level for the approximate integration of the Schrödinger equation

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A Runge-Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level 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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A parametric symmetric linear four-step method 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 family of explicit linear six-step methods with vanished phase-lag and its first derivative

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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 high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equation

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A high algebraic order predictor-corrector explicit method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation and related problems

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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 predictor-corrector explicit four-step method with vanished phase-lag and its first, second and third 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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An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown

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

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Symplectic methods for the numerical solution of the radial Schrödinger equation

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Symplectic methods of fifth order for the numerical solution of the radial Schrödinger equation

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New second-order exponentially and trigonometrically fitted symplectic integrators for the numerical solution of the time-independent Schrödinger equation

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Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation

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Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation

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Symplectic integrators for the numerical solution of the Schrödinger equation

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Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems

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Newton--Cotes formulae for long-time integration.

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High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the 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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High-order closed Newton-Cotes trigonometrically-fitted formulae for long-time integration of orbital problems

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

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New stable 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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New open modified Newton Cotes type formulae as multilayer symplectic integrators

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A Fifth-order Symplectic Trigonometrically Fitted Partitioned Runge-Kutta Method

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Families of third and fourth algebraic order trigonometrically fitted symplectic methods for the numerical integration of Hamiltonian systems

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Computation of the eigenvalues of the Schrödinger equation by symplectic and trigonometrically fitted symplectic partitioned Runge-Kutta methods

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New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation

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A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods

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TWO NEW PHASE-FITTED SYMPLECTIC PARTITIONED RUNGE–KUTTA METHODS

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A new approach on the construction of trigonometrically fitted two step hybrid methods

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Modified two‐step hybrid methods for the numerical integration of oscillatory problems

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Symplectic partitioned Runge-Kutta methods with minimal phase-lag

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Family of twelve steps exponential fitting symmetric multistep methods for the numerical solution of the Schrödinger equation

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Trigonometrically fitted predictor--corrector methods for IVPs with oscillating solutions

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A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions

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Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution.

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Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation

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New P-stable eighth algebraic order exponentially-fitted methods for the numerical integration of the Schrödinger equation

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A family of trigonometrically-fitted symmetric methods for the efficient solution of the Schrödinger equation and related problems

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Exponentially-fitted multiderivative methods for the numerical solution of the Schrödinger equation

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A four-step exponentially fitted method for the numerical solution of the Schrödinger equation

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

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A family of four-step trigonometrically-fitted methods and its application to the Schrödinger equation

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A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solution

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Sixth algebraic order trigonometrically fitted predictor-corrector methods for the numerical solution of the radial Schrödinger equation

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The numerical solution of the radial Schrödinger equation via a trigonometrically fitted family of seventh algebraic order predictor-corrector methods

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P-stable linear symmetric multistep methods for periodic initial-value problems

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A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equation

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High-order predictor--corrector of exponential fitting for the \(N\)-body problems

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Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutions

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Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs

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A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problems

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On finite difference methods for the solution 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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A multistep method with optimal properties for second order differential equations

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Two stages six-step method with eliminated phase-lag and its first, second, third and fourth derivatives for the approximation 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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A family of embedded Runge-Kutta formulae

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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/S10910-017-0812-2

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Sitelinks

Mathematics(1 entry)

mardi Publication:1742794

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