Numerical integration methods for stochastic wave function equations
type: Item
instance of: scholarly article
title: Numerical integration methods for stochastic wave function equations
zbMATH Open document ID: 0967.65003
DOI: 10.1016/S0010-4655(00)00135-1
author: Heinz-Peter Breuer
author: Uwe Dorner
author: Francesco Petruccione
published in: Computer Physics Communications
publication date: 2001-09-04T00:00:00Z
review text: Four methods for numerically solving stochastic differential equations (SDEs) are compared for two examples from quantum mechanics of open systems. The methods examined are the Euler-Maruyama scheme, a stochastic Heun scheme, a stochastic Runge-Kutta order 4 scheme, and an explicit order 2 weak scheme due to Platen [cf. \textit{P. E. Kloeden} and \textit{E. Platen}, Numerical solution of stochastic differential equations (1992; Zbl 0752.60043)]. The examples are an SDE arising from a damped harmonic oscillator and an SDE arising from a two-level atom driven by an external single mode laser field on resonance. It is found that Platen's method yields the best results, especially when comparing accuracy per unit of CPU time required; and that the stochastic Heun and stochastic Runge-Kutta methods have no significant advantage over the Euler-Maruyama method.
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 81-08
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 1552645
zbMATH Keywords: stochastic wave function equations
zbMATH Keywords: stochastic Heun method
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: quantum mechanics of open systems
zbMATH Keywords: Euler-Maruyama scheme
zbMATH Keywords: damped harmonic oscillator
zbMATH Keywords: stochastic Runge-Kutta methods
MaRDI profile type: Publication
full work available at URL: s0010-4655(00)00135-1
OpenAlex ID: W2028425295
description: scientific article; zbMATH DE number 1552645