Work

Higher Strong Order Methods for Itô SDEs on Matrix Lie Groups

Year: 2021

Type: preprint

Abstract: In this paper we present a general procedure for designing higher strong order methods for Itô stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge-Kutta--Munthe-Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge-Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2102.04131

Authors: Muniz, Michelle, Ehrhardt, Matthias, Günther, Michael, Winkler, Renate

Institution: University of Wuppertal

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Dublin City University, Deutscher Akademischer Austauschdienst

OpenAlex ID: W3129057574

Cites: 26

Cited by:

Related to: 20