Higher Strong Order Methods for Itô SDEs on Matrix Lie Groups

2021/02/08 by Michelle Muniz, Muniz, Michelle, Matthias Ehrhardt +5
Computer Science · Engineering · Mathematics · #60H10 #70G65 #91G80 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2102.04131

openalex publication_date 2021/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the exponential solution of differential equations for a linear operator

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