CP methods for the Schrödinger equation

DOI10.1016/S0377-0427(00)00478-7zbMath0971.65067MaRDI QIDQ1841966

L. Gr. Ixaru

Publication date: 1 November 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical exampleerror analysisone dimensional Schrödinger equationpiecewise perturbation methodsconstant perturbation methods

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (22)

A posteriori error bounds for the approximate solution of second-order ODEs by piecewise coefficients perturbation methods ⋮ Uniform and high-order discretization schemes for Sturm-Liouville problems via Fer streamers ⋮ Numerical methods for the eigenvalue determination of second-order ordinary differential equations ⋮ The accurate numerical solution of the Schrödinger equation with an explicitly time-dependent Hamiltonian ⋮ Coefficients perturbation methods for higher-order differential equations ⋮ Correction of eigenvalues estimated by the Legendre-Gauss tau method ⋮ Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics ⋮ The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations ⋮ An exponentially convergent functional-discrete method for solving Sturm-Liouville problems with a potential including the Dirac \(\delta\)-function ⋮ Numerical solution of Sturm-Liouville problems via Fer streamers ⋮ Solving Sturm-Liouville problems by piecewise perturbation methods, revisited ⋮ CP methods and the evaluation of negative energy Coulomb Whittaker functions ⋮ CP methods of higher order for Sturm-Liouville and Schrödinger equations ⋮ \(CPM\{P,N\}\) methods extended for the solution of coupled channel Schrödinger equations ⋮ Solution of the Schrödinger equation over an infinite integration interval by perturbation methods, revisited ⋮ Efficient computation of the Airy propagators ⋮ Fast LP method for the Schrödinger equation ⋮ An improved tau method for a class of Sturm-Liouville problems ⋮ Limit cycles in nonlinear excitation of clusters of classical oscillators ⋮ Boundary value methods as an extension of Numerov's method for Sturm-Liouville eigenvalue estimates ⋮ LILIX -- a package for the solution of the coupled channel Schrödinger equation ⋮ Matslise 2.0

Uses Software

• SLDRIVER

Cites Work

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• Automatic solution of Sturm-Liouville problems using the Pruess method
• Piecewise perturbation methods for calculating eigensolutions of a complex optical potential
• CP methods for the Schrödinger equation revisited
• SLCPM12 -- a program for solving regular Sturm-Liouville problems
• A new method for the solution of the Schrödinger equation
• The error analysis of the algebraic method for solving the Schrödinger equation
• Uniform estimation of the eigenvalues of Sturm–Liouville problems
• Automatic Solution of the Sturm-Liouville Problem
• Mathematical software for Sturm-Liouville problems
• Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation

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