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

Anton, Cristina

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

Author

Anton, Cristina

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