Parareal algorithms applied to stochastic differential equations with conserved quantities

2016/09/27 by Liying Zhang, Zhang, Liying, Weien Zhou +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1609.08299

openalex publication_date 2016/09/27 · openalex created_date 2016/10/07 · openalex updated_date 2026/08/01

Abstract

In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are introduced as the coarse and fine propagators. Second, we also apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm. Finally, three numerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration, and preservation in conserved quantities of model systems.

Citations

• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Symmetric parareal algorithms for Hamiltonian systems

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