Work

Conservative Methods for Stochastic Differential Equations with a Conserved Quantity

Year: 2016

Type: article

Abstract: This paper proposes a novel conservative method for the numerical approximation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is 1 if noises are commutative and that the weak order is 1 in the general case. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results.

Source: International Journal of Numerical Analysis and Modeling

DOI: 10.4208/ijnam.v13.n3.p435

Authors: C.-C. Chen, D. Cohen, J.-L. Hong

Institutions: Chinese Academy of Sciences, Purdue University West Lafayette, Umeå University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Vetenskapsrådet, Umeå Universitet

Awards: G2822134640, G3982985774, G757509706