Projection methods for stochastic differential equations with conserved quantities

TL;DR

This paper develops high-order projection-based numerical methods for stochastic differential equations that preserve conserved quantities, achieving strong convergence orders up to 2, validated through numerical experiments.

Contribution

It introduces projection methods capable of preserving conserved quantities in stochastic differential equations with high strong convergence orders.

Findings

Mean-square convergence order can reach 1.5 or 2

Projection methods outperform traditional methods in preserving invariants

Numerical experiments confirm the effectiveness of the proposed methods

Abstract

In this paper, we consider the numerical methods preserving single or multiple conserved quantities, and these methods are able to reach high order of strong convergence simultaneously based on some kinds of projection methods. The mean-square convergence orders of these methods under certain conditions are given, which can reach order 1.5 or even 2 according to the supporting methods embedded in the projection step. Finally, three numerical experiments are taken into account to show the superiority of the projection methods.