stochastic-schroedinger-equation
Numerical simulation of the stochastic Schroedinger equation for the paper 'Pathwise uniform convergence of time discretisation schemes for SPDEs' by Katharina Klioba and Mark Veraar
https://github.com/k-klioba/stochastic-schroedinger-equation
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Repository
Numerical simulation of the stochastic Schroedinger equation for the paper 'Pathwise uniform convergence of time discretisation schemes for SPDEs' by Katharina Klioba and Mark Veraar
Basic Info
- Host: GitHub
- Owner: k-klioba
- License: gpl-3.0
- Language: MATLAB
- Default Branch: main
- Size: 35.8 MB
Statistics
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 3
Metadata Files
README.md
stochastic-schroedinger-equation
Description
This code numerically solves the linear stochastic Schroedinger equation with additive or multiplicative Gaussian noise. For the spatial discretisation, a spectral Galerkin approach is used, and for the temproal discretisation, the exponential Euler, implicit Euler, and Crank-Nicolson method are compared. The numerical convergence rates obtained correspond to the analytical convergence rates proven in 'Pathwise Uniform Convergence of Time Discretisation Schemes for SPDEs' by Katharina Klioba and Mark Veraar, see arXiv 2303.00411.
How to reproduce the data and plots
After cloning this repository, run the following programs in Matlab. Version R2022b or newer is advised.
- To reproduce the numerical convergence rates for the case of additive noise, run schroedinger_spectral_additive.m.
- To reproduce the numerical convergence rates for the case of multiplicative noise, run schroedinger_spectral_multiplicative.m.
- To recreate Figure 1 from the paper, run plotpaperfigure.m. This requires the files ErrEXP_additive_samples100_M1024_dt25912.mat and ErrEXP_multiplicative_samples100_M1024_dt25912.mat from this repository.
Requirements
Installation of Matlab version R2022b or newer is required.
Authors and acknowledgment
Authors: Katharina Klioba (Hamburg University of Technology) and Mark Veraar (Delft University of Technology)
The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).
License
GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007
Owner
- Login: k-klioba
- Kind: user
- Repositories: 1
- Profile: https://github.com/k-klioba
Citation (CITATION.cff)
# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!
cff-version: 1.2.0
title: Stochastic Schroedinger equation
message: >-
If you use this software, please cite it using the
metadata from this file.
type: software
authors:
- given-names: Katharina
family-names: Klioba
email: Katharina.klioba@tuhh.de
affiliation: Hamburg University of Technology
orcid: 'https://orcid.org/0009-0002-7946-917X'
- given-names: Mark
name-particle: C.
family-names: Veraar
email: M.C.Veraar@tudelft.nl
affiliation: Delft University of Technology
orcid: 'https://orcid.org/0000-0003-3167-7471'
repository-code: >-
https://github.com/k-klioba/stochastic-schroedinger-equation
abstract: >-
Numerical simulation of the linear stochastic Schroedinger
equation with additive and multiplicative Gaussian noise
for the paper 'Pathwise uniform convergence of time
discretisation schemes for SPDEs' by Katharina Klioba and
Mark Veraar
keywords:
- stochastic Schroedinger equation
- pathwise uniform error
- optimal convergence rates
- additive noise
- multiplicative noise
license: CC-BY-4.0
version: v1.0
date-released: '2024-07-12'