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- Title
Structure-preserving stochastic conformal exponential integrator for linearly damped stochastic differential equations.
- Authors
Yang, Guoguo; Ma, Qiang; Li, Xuliang; Ding, Xiaohua
- Abstract
In this paper, we study the linearly damped stochastic differential equations, which have the invariants satisfying a linear differential equation whose coefficients are linear constant or time-dependent. A stochastic exponential integrator is proposed for linearly damped stochastic differential equations to preserve their intrinsic properties. Then, the conformal symplecticity of stochastic Hamiltonian systems with linearly damped term is studied. For linearly damped stochastic Hamiltonian systems, it is shown that the stochastic exponential integrator can exactly preserve conformal quadratic invariant and conformal symplecticity. The mean-square convergence order of the method is analyzed. Numerical tests present the good performance of the proposed stochastic exponential integrator in structure-preserving.
- Subjects
STOCHASTIC differential equations; EXPONENTIAL functions; INTEGRATORS; HAMILTONIAN systems; NUMERICAL analysis; CONFORMAL mapping
- Publication
Calcolo, 2019, Vol 56, Issue 1, p1
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-019-0302-y