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