A new hybrid imbedded variable-step procedure for the numerical integration of the Schrödinger equation
type: Item
instance of: scholarly article
title: A new hybrid imbedded variable-step procedure for the numerical integration of the Schrödinger equation
zbMATH Open document ID: 0932.65082
DOI: 10.1016/S0898-1221(98)00116-3
publication date: 2000-03-21T00:00:00Z
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1357891
zbMATH Keywords: \(P\)-stability
zbMATH Keywords: numerical examples
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: second-order oscillatory initial value problem
zbMATH Keywords: phase-lag
zbMATH Keywords: imbedded technique
zbMATH Keywords: variable-step procedure
author: T. E. Simos
MaRDI profile type: Publication
cites work: AN EXPLICIT HIGH ORDER PREDICTOR-CORRECTOR METHOD FOR PERIODIC INITIAL VALUE PROBLEMS
cites work: Solving Ordinary Differential Equations I
cites work: Symmetric Multistip Methods for Periodic Initial Value Problems
cites work: High-order P-stable multistep methods
cites work: A variable step method for the numerical integration of the one- dimensional Schrödinger equation
cites work: The numerical solution of coupled differential equations arising from the Schrödinger equation
cites work: A sixth order tridiagonal finite difference method for non-linear two-point boundary value problems
cites work: Q3283176
cites work: A sixth-order exponentially fitted method for the numerical solution of the radial Schrödinger equation
cites work: An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields
cites work: Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem
cites work: Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation
cites work: Coleman's method maximally adapted to the Schrödinger equation
cites work: Piecewise perturbation methods for calculating eigensolutions of a complex optical potential
cites work: An efficient algorithm for solving coupled Schrödinger type ODE's, whose potentials include \(\delta\)-functions
cites work: A one-step method for direct integration of structural dynamic equations
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
cites work: Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y''=f(t,y)\)
cites work: An explicit sixth-order method with phase-lag of order eight for \(y''=f(t,y)\)
cites work: Phase properties of high order, almost P-stable formulae
cites work: Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems
cites work: Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
cites work: Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
cites work: Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation
cites work: A four-step phase-fitted method for the numerical integration of second order initial-value problems
cites work: A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-value problem
cites work: New variable-step procedure for the numerical integration of the one- dimensional Schrödinger equation
cites work: A NEW NUMEROV-TYPE METHOD FOR COMPUTING EIGENVALUES AND RESONANCES OF THE RADIAL SCHRÖDINGER EQUATION
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1357891