Generating functions for stochastic symplectic methods

DOI10.3934/dcds.2014.34.1211zbMath1278.65006OpenAlexW2332515471MaRDI QIDQ379801

Lijin Wang, Jialin Hong

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2014.34.1211

zbMATH Keywords

generating functionsnumerical examplessymplectic integrationstochastic Hamiltonian systemsstochastic symplectic methodsHamilton-Jacobi PDEssymplecticity

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Ordinary differential equations and systems with randomness (34F05) Generation, random and stochastic difference and differential equations (37H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (14)

Two Novel Classes of Arbitrary High-Order Structure-Preserving Algorithms for Canonical Hamiltonian Systems ⋮ Positivity-preserving symplectic methods for the stochastic Lotka-Volterra predator-prey model ⋮ Stochastic discrete Hamiltonian variational integrators ⋮ Modified equations for weakly convergent stochastic symplectic schemes via their generating functions ⋮ Splitting integrators for stochastic Lie–Poisson systems ⋮ Arbitrary high-order EQUIP methods for stochastic canonical Hamiltonian systems ⋮ High Order Conformal Symplectic and Ergodic Schemes for the Stochastic Langevin Equation via Generating Functions ⋮ Numerical investigation of stochastic canonical Hamiltonian systems by high order stochastic partitioned Runge-Kutta methods ⋮ Asymptotically-Preserving Large Deviations Principles by Stochastic Symplectic Methods for a Linear Stochastic Oscillator ⋮ Long-term adaptive symplectic numerical integration of linear stochastic oscillators driven by additive white noise ⋮ Explicit pseudo-symplectic methods for stochastic Hamiltonian systems ⋮ A Note on the Generating Function Method ⋮ Structure-Preserving Numerical Methods for Stochastic Poisson Systems ⋮ A review on stochastic multi-symplectic methods for stochastic Maxwell equations

Cites Work

• The stochastic Hamilton-Jacobi equation
• Numerical simulation of a linear stochastic oscillator with additive noise
• Symplectic conditions and stochastic generating functions of stochastic Runge-Kutta methods for stochastic Hamiltonian systems with multiplicative noise
• Predictor-corrector methods for a linear stochastic oscillator with additive noise
• Order Conditions of Stochastic Runge--Kutta Methods by B-Series
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Discrete Hamiltonian variational integrators
• Symplectic Integration of Hamiltonian Systems with Additive Noise
• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
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