Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems - Anton, Cristina (My University, 2023)
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.
Keywords: stochastic Hamiltonian systems; stochastic Runge-Kutta methods; quadratic invariants; symplectic integration; pseudo-symplectic method