A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation
type: Item
instance of: scholarly article
title: A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation
zbMATH Open document ID: 1447.81112
author: Shiwei Liu
author: Juan Zheng
author: Yonglei Fang
publication date: 2013-04-08T00:00:00Z
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81-08
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 81U05
zbMATH DE Number: 6151493
zbMATH Keywords: embedded Runge-Kutta methods
zbMATH Keywords: error analysis
zbMATH Keywords: Schrödinger equation
MaRDI profile type: Publication
full work available at URL: s10910-012-0127-2
OpenAlex ID: W2076684813
cites work: Exponentially-fitted explicit Runge-Kutta methods
cites work: An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
cites work: An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems
cites work: A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions
cites work: A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
cites work: Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics
cites work: An optimized Runge-Kutta method for the solution of orbital problems
cites work: Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
cites work: A NEW METHODOLOGY FOR THE CONSTRUCTION OF OPTIMIZED RUNGE–KUTTA–NYSTRÖM METHODS
cites work: An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems
cites work: An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems
cites work: 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
cites work: A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
cites work: Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions
cites work: Optimized Runge-Kutta pairs for problems with oscillating solutions
cites work: Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation
cites work: A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrödinger equation
cites work: Q5950903
cites work: Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation
cites work: A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation
cites work: Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions
cites work: Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equation
cites work: A family of multiderivative methods for the numerical solution of the Schrödinger equation
cites work: A new Numerov-type method for the numerical solution of the Schrödinger equation
cites work: High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation
cites work: Mulitstep methods with vanished phase-lag and its first and second derivatives for the numerical integration of the Schrödinger equation
cites work: A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation
cites work: Optimizing a hybrid two-step method for the numerical solution of the Schrödinger equation and related problems with respect to phase-lag
cites work: A family of ten-step methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation
cites work: A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation
cites work: A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equation
cites work: A new hybrid two-step method with vanished phase-lag and its first and second derivatives for the numerical solution of the Schrödinger equation and related problems
cites work: A new two-step hybrid method for the numerical solution of the Schrödinger equation
cites work: Trigonometrically fitted predictor--corrector methods for IVPs with oscillating solutions
cites work: A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions
cites work: Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solution.
cites work: Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation
cites work: A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
cites work: A variable-step Numerov method for the numerical solution of the Schrödinger equation
cites work: A new eighth-order A-stable method for solving differential systems arising in chemical reac\-tions
cites work: Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
cites work: Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
cites work: On the stability of exponential fitting BDF algorithms
cites work: An embedded phase-fitted modified Runge-Kutta method for the numerical integration of the radial Schrödinger equation
cites work: An embedded Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation
cites work: New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation
cites work: Chebyshevian multistep methods for ordinary differential equations
cites work: A family of embedded Runge-Kutta formulae
cites work: Solving Ordinary Differential Equations I
cites work: Runge-Kutta methods adapted to the numerical integration of oscillatory problems
cites work: Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation
cites work: AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION
cites work: Q4679151
cites work: A variable step method for the numerical integration of the one- dimensional Schrödinger equation
cites work: Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
cites work: On the frequency choice in trigonometrically fitted methods
DOI: 10.1007/S10910-012-0127-2
published in: Journal of Mathematical Chemistry
description: scientific article; zbMATH DE number 6151493