A new embedded 4(3) pair of modified two-derivative Runge-Kutta methods with FSAL property for the numerical solution of the Schrödinger equation
type: Item
instance of: scholarly article
title: A new embedded 4(3) pair of modified two-derivative Runge-Kutta methods with FSAL property for the numerical solution of the Schrödinger equation
zbMATH Open document ID: 1417.81171
author: Shiwei Liu
author: Juan Zheng
author: Yonglei Fang
publication date: 2019-07-01T00:00:00Z
Mathematics Subject Classification ID: 81V55
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 7075220
zbMATH Keywords: embedded TDRK pair
zbMATH Keywords: Lennard-Jones potential
zbMATH Keywords: Schrödinger equation
MaRDI profile type: Publication
full work available at URL: s10910-018-0974-6
OpenAlex ID: W2898839722
cites work: Chebyshevian multistep methods for ordinary differential equations
cites work: Symmetric Multistip Methods for Periodic Initial Value Problems
cites work: Numerov made explicit has better stability
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
cites work: An exponentially-fitted high order method for long-term integration of periodic initial-value problems
cites work: Parameter uniform numerical method for singularly perturbed turning point problems exhibiting boundary layers.
cites work: Exponential fitting BDF algorithms: explicit and implicit 0-stable methods
cites work: On the numerical solution of the heat conduction equations subject to nonlocal conditions
cites work: A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems
cites work: An explicit four-step method with vanished phase-lag and its first and second derivatives
cites work: A new explicit hybrid four-step method with vanished phase-lag and its derivatives
cites work: A variable step method for the numerical integration of the one- dimensional Schrödinger equation
cites work: Variable stepsize implementation of multistep methods for \(y\prime\prime =f(x,y,y^{\prime})\)
cites work: An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
cites work: Exponentially fitted Runge-Kutta methods
cites work: Triangular splitting implementation of RKN‐type Fourier collocation methods for second‐order differential equations
cites work: Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems
cites work: Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations
cites work: Arbitrary-order functionally fitted energy-diminishing methods for gradient systems
cites work: Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations
cites work: Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations
cites work: Exponential Fourier Collocation Methods for Solving First-Order Differential Equations
cites work: Global error bounds of one-stage extended RKN integrators for semilinear wave equations
cites work: The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations
cites work: Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations
cites work: New energy-preserving algorithms for nonlinear Hamiltonian wave equation equipped with Neumann boundary conditions
cites work: Explicit two-step methods with minimal phase-lag for the numerical integration of special second-order initial-value problems and their application to the one-dimensional 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: A modified phase-fitted Runge-Kutta method for the numerical solution of the Schrödinger equation
cites work: An embedded phase-fitted modified Runge-Kutta method for the numerical integration of the radial Schrödinger equation
cites work: Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\)
cites work: Q4679151
cites work: AN EMBEDDED 5(4) PAIR OF MODIFIED EXPLICIT RUNGE–KUTTA METHODS FOR THE NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION
cites work: A new modified embedded 5(4) pair of explicit Runge-Kutta methods for the numerical solution of the Schrödinger equation
cites work: A new embedded 5(3) pair of modified Runge-Kutta-Nyström methods for the numerical solution of the Schrödinger equation
cites work: On explicit two-derivative Runge-Kutta methods
cites work: Stability and phase-lag analysis of explicit Runge-Kutta methods with variable coefficients for oscillatory problems
cites work: A Runge-Kutta-Nyström pair for the numerical integration of perturbed oscillators
cites work: A \(5(3)\) pair of explicit Runge-Kutta-Nyström methods for oscillatory problems
DOI: 10.1007/S10910-018-0974-6
published in: Journal of Mathematical Chemistry
description: scientific article; zbMATH DE number 7075220