Preservation of quadratic invariants of stochastic differential equations via Runge-Kutta methods

DOI10.1016/j.apnum.2014.08.003zbMath1302.65027OpenAlexW2068020312MaRDI QIDQ465120

Jialin Hong, Dongsheng Xu, Peng Wang

Publication date: 31 October 2014

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2014.08.003

zbMATH Keywords

strong convergenceweak convergencestochastic differential equationsRunge-Kutta methodsnumerical experimentquadratic invariantssymplecticity

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) 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)

Related Items (23)

Weak stochastic Runge-Kutta Munthe-Kaas methods for finite spin ensembles ⋮ Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise ⋮ Stochastic multi-symplectic Runge-Kutta methods for stochastic Hamiltonian PDEs ⋮ Long-Term Analysis of Stochastic Hamiltonian Systems Under Time Discretizations ⋮ Stochastic discrete Hamiltonian variational integrators ⋮ General order conditions for stochastic partitioned Runge-Kutta methods ⋮ Order conditions for stochastic Runge-Kutta methods preserving quadratic invariants of Stratonovich SDEs ⋮ Explicit pseudo-symplectic Runge-Kutta methods for stochastic Hamiltonian systems ⋮ Numerical solution of stochastic quantum master equations using stochastic interacting wave functions ⋮ High order numerical integrators for single integrand Stratonovich SDEs ⋮ Modified averaged vector field methods preserving multiple invariants for conservative stochastic differential equations ⋮ Perturbative analysis of stochastic Hamiltonian problems under time discretizations ⋮ Drift-preserving numerical integrators for stochastic Hamiltonian systems ⋮ Efficient Stochastic Runge-Kutta Methods for Stochastic Differential Equations with Small Noises ⋮ Cheap arbitrary high order methods for single integrand SDEs ⋮ Asymptotically optimal approximation of some stochastic integrals and its applications to the strong second-order methods ⋮ High-order stochastic symplectic partitioned Runge-Kutta methods for stochastic Hamiltonian systems with additive noise ⋮ Projection methods for stochastic differential equations with conserved quantities ⋮ Tamed Runge-Kutta methods for SDEs with super-linearly growing drift and diffusion coefficients ⋮ STOCHASTIC PARTITIONED AVERAGED VECTOR FIELD METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH A CONSERVED QUANTITY ⋮ Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants ⋮ A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations ⋮ Discrete gradient methods and linear projection methods for preserving a conserved quantity of stochastic differential equations

Cites Work

• Three-stage stochastic Runge-Kutta methods for stochastic differential equations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise.
• Energy conservative stochastic difference scheme for stochastic Hamilton dynamical systems
• Second order Runge-Kutta methods for Stratonovich stochastic differential equations
• Predictor-corrector methods for a linear stochastic oscillator with additive noise
• Order Conditions of Stochastic Runge--Kutta Methods by B-Series
• High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
• Stability of Runge-Kutta Methods for Trajectory Problems
• Discrete Gradient Approach to Stochastic Differential Equations with a Conserved Quantity
• The Invariance of Asymptotic Laws of Linear Stochastic Systems under Discretization
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