A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation

DOI10.1007/s10910-014-0328-yzbMath1301.65073OpenAlexW2167120504MaRDI QIDQ460890

Juan Zheng, Shiwei Liu, Yong Lei Fang

Publication date: 9 October 2014

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-014-0328-y

zbMATH Keywords

numerical resultsSchrödinger equationexponential fittinglocal truncation errorresonance problemelastic scattering phase-shift problemembedded modified Runge-Kutta-Nyström methods

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (1)

A new embedded 4(3) pair of modified two-derivative Runge-Kutta methods with FSAL property for the numerical solution of the Schrödinger equation

Cites Work

• Unnamed Item
• A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problems
• A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems
• A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation
• High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation
• New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation
• Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
• A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
• Comparison of some special optimized fourth-order Runge-Kutta methods for the numerical solution of the Schrödinger equation
• A Runge-Kutta-Nyström pair for the numerical integration of perturbed oscillators
• Exponential fitting BDF-Runge-Kutta algorithms
• Variable stepsize Störmer-Cowell methods
• An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems
• An embedded phase-fitted modified Runge-Kutta method for the numerical integration of the radial Schrödinger equation
• On the frequency choice in trigonometrically fitted methods
• A \(5(3)\) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems
• A new Numerov-type method for the numerical solution of the Schrödinger equation
• A variable step method for the numerical integration of the one- dimensional Schrödinger equation
• An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
• An embedded exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation and related periodic initial-value problems
• Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions
• Symmetric eighth algebraic order methods with minimal phase-lag for the numerical solution of the Schrödinger equation
• 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
• An optimized Runge-Kutta method for the solution of orbital problems
• Family of twelve steps exponential fitting symmetric multistep methods for the numerical solution of the Schrödinger equation
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• Runge-Kutta methods adapted to the numerical integration of oscillatory problems
• An optimized explicit Runge-Kutta-Nyström method for the numerical solution of orbital and related periodical initial value problems
• Exponentially-fitted explicit Runge-Kutta methods
• Exponential fitting BDF algorithms and their properties
• A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation
• A variable-step Numerov method for the numerical solution of the Schrödinger equation
• Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrödinger equation
• Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
• Chebyshevian multistep methods for ordinary differential equations
• Frequency evaluation for exponentially fitted Runge-Kutta methods
• AN EMBEDDED RUNGE–KUTTA METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION
• A NEW MODIFIED RUNGE–KUTTA–NYSTRÖM METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION AND RELATED PROBLEMS
• A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrodinger equation
• Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies
• Solving Ordinary Differential Equations I
• A modified Runge–Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation and related problems
• Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods
• A family of P-stable eighth algebraic order methods with exponential fitting facilities

This page was built for publication: A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation