A new six-step algorithm with improved properties for the numerical solution of second order initial and/or boundary value problems (Q2636424)

scientific article

Language	Label	Description	Also known as
English	A new six-step algorithm with improved properties for the numerical solution of second order initial and/or boundary value problems	scientific article

Statements

instance of

scholarly article

0 references

title

A new six-step algorithm with improved properties for the numerical solution of second order initial and/or boundary value problems (English)

0 references

0 references

0 references

5 June 2018

0 references

zbMATH Keywords

Schrödinger equation

0 references

multistep methods

0 references

multistage methods

0 references

interval of periodicity

0 references

phase-lag

0 references

phase-fitted

0 references

derivatives of the phase-lag

0 references

describes a project that uses

LaTeX

0 references

MaRDI profile type

Publication

0 references

full work available at URL

https://doi.org/10.1007/s10910-017-0840-y

0 references

cites work

Q5569399

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström method

0 references

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

0 references

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

0 references

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

0 references

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

0 references

Optimized Runge-Kutta pairs for problems with oscillating solutions

0 references

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

0 references

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

0 references

Symmetric Multistip Methods for Periodic Initial Value Problems

0 references

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

0 references

On modified Runge-Kutta trees and methods

0 references

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

0 references

Q4604885

0 references

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

0 references

A new family of 7 stages, eighth-order explicit Numerov-type methods

0 references

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

0 references

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

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

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

A family of explicit linear six-step methods with vanished phase-lag and its first derivative

0 references

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

0 references

Q3466063

0 references

Q5739308

0 references

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

0 references

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

0 references

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

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

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

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

0 references

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

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 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

0 references

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

0 references

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

0 references

An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown

0 references

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

0 references

Symplectic methods for the numerical solution of the radial Schrödinger equation

0 references

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

0 references

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

0 references

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

0 references

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

0 references

Symplectic integrators for the numerical solution of the Schrödinger equation

0 references

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

0 references

Newton--Cotes formulae for long-time integration.

0 references

High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation

0 references

Q3184863

0 references

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

0 references

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

0 references

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

0 references

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

0 references

New open modified Newton Cotes type formulae as multilayer symplectic integrators

0 references

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

0 references

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

0 references

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

0 references

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

0 references

A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods

0 references

TWO NEW PHASE-FITTED SYMPLECTIC PARTITIONED RUNGE–KUTTA METHODS

0 references

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

0 references

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

0 references

Symplectic partitioned Runge-Kutta methods with minimal phase-lag

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

On finite difference methods for the solution of the Schrödinger equation

0 references

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

0 references

Two stages six-step method with eliminated phase-lag and its first, second, third and fourth derivatives for the approximation of the Schrödinger equation

0 references

High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation

0 references

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

0 references

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

0 references

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.

0 references

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

0 references

Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002), Alicante, Spain, 20--25 September 2002

0 references

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

0 references

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

0 references

A multistep method with optimal properties for second order differential equations

0 references

Families of Runge-Kutta-Nystrom Formulae

0 references

A family of embedded Runge-Kutta formulae

0 references

published in

Journal of Mathematical Chemistry

0 references

Identifiers

zbMATH Open document ID

1447.81113

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

10.1007/S10910-017-0840-Y

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:2636424