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Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems

Faculty Advisor

Date

2023

Keywords

stochastic Hamiltonian systems, stochastic Runge-Kutta methods, quadratic invariants, symplectic integration, pseudo-symplectic method

Abstract (summary)

We give conditions for stochastic Runge-Kutta methods to near preserve quadratic invariants, and we discuss the associated simpli ed order conditions. For stochastic Hamiltonian systems we propose a systematic approach to construct explicit stochastic Runge-Kutta pseudo-symplectic schemes. Our approach is based on colored trees and B-series. We construct some pseudosymplectic stochastic Runge-Kutta methods with strong convergence order, and we illustrate numerically the long term performance of the proposed schemes.

Publication Information

Cristina A. (2023). Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems. Applied Numerical Mathematics, 185, 2023, 18-37. https://doi.org/10.1016/j.apnum.2022.11.013

Notes

Item Type

Article Post-Print

Language

Rights

Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Embargoed Until:

March 31, 2025

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