Work

On Magnus Integrators for Time-Dependent Schrödinger Equations

Year: 2003

Type: article

Abstract: Numerical methods based on the Magnus expansion are an efficient class of integrators for Schrödinger equations with time-dependent Hamiltonian. Though their derivation assumes an unreasonably small time step size, as would be required for a standard explicit integrator, the methods perform well even for much larger step sizes. This favorable behavior is explained, and optimal-order error bounds are derived that require no or only mild restrictions of the step size. In contrast to standard integrators, the error does not depend on higher time derivatives of the solution, which is in general highly oscillatory.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/s0036142902403875

Authors: Marlis Hochbruck, Christian Lubich

Institutions: Heinrich Heine University Düsseldorf, University of Tübingen

Language: English

Topic: Numerical Solvers for Ordinary Differential Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Leibniz-Gemeinschaft

OpenAlex ID: W1973055673

FWCI: 6.002

Cites: 13

Cited by: 120

Related to: 8