An efficient and economical high order method for the numerical approximation of the Schrödinger equation (Q1694275)

scientific article; zbMATH DE number 6833425

Language	Label	Description	Also known as
English	An efficient and economical high order method for the numerical approximation of the Schrödinger equation	scientific article; zbMATH DE number 6833425

Statements

instance of

scholarly article

0 references

title

An efficient and economical high order method for the numerical approximation of the Schrödinger equation (English)

0 references

0 references

0 references

1 February 2018

0 references

zbMATH Keywords

phase-lag

0 references

derivative of the phase-lag

0 references

oscillating solution

0 references

symmetric

0 references

hybrid

0 references

multistep

0 references

Schrödinger equation

0 references

boudnary value problem

0 references

numerical example

0 references

error analysis

0 references

stability

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/s10910-017-0757-5

0 references

cites work

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

0 references

Symmetric Multistip Methods for Periodic Initial Value Problems

0 references

A finite-difference method 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

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

0 references

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

0 references

An efficient and computational effective method for second order problems

0 references

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

0 references

A four-step phase-fitted method for the numerical integration of second order initial-value problems

0 references

High-order P-stable multistep methods

0 references

Q4002473

0 references

Stabilization of Cowell's method

0 references

Q3184862

0 references

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

0 references

An exponentially-fitted and trigonometrically-fitted method for the numerical solution of periodic initial-value problems.

0 references

A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems

0 references

Chebyshevian multistep methods for ordinary differential equations

0 references

Phase properties of high order, almost P-stable formulae

0 references

Symplectic integrators for the numerical solution of the Schrödinger equation

0 references

Newton--Cotes formulae for long-time integration.

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

0 references

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

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

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

0 references

New stable closed Newton-Cotes trigonometrically fitted formulae for long-time integration

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 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

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

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

0 references

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

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

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 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

A new optimized symmetric 8-step semi-embedded predictor-corrector method for the numerical solution of the radial Schrödinger equation and related orbital problems

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

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

0 references

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

0 references

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

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

0 references

On modified Runge-Kutta trees and methods

0 references

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

0 references

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

0 references

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

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

Q3466063

0 references

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

0 references

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

0 references

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

0 references

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

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

0 references

Families of Runge-Kutta-Nystrom Formulae

0 references

A family of embedded Runge-Kutta formulae

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

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

0 references

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

0 references

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

0 references

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

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 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

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

0 references

Q4956476

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

Q5739308

0 references

An efficient numerical method for the 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 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

0 references

published in

Journal of Mathematical Chemistry

0 references

Identifiers

zbMATH Open document ID

1383.65083

0 references

Mathematics Subject Classification ID

0 references

0 references

0 references

0 references

0 references

0 references

0 references

0 references

10.1007/S10910-017-0757-5

0 references

Sitelinks

Mathematics(1 entry)

mardi Publication:1694275