A class of orthogonal integrators for stochastic differential equations
Journal of Computational and Applied Mathematics
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A class of orthogonal integrators for stochastic differential equations
Journal of Computational and Applied Mathematics
A Second-Order Strong Method for the Langevin Equations with Holonomic Constraints
SIAM Journal on Scientific Computing
Discrete Gradient Approach to Stochastic Differential Equations with a Conserved Quantity
SIAM Journal on Numerical Analysis
Original articles: On the numerical discretisation of stochastic oscillators
Mathematics and Computers in Simulation
Predictor-corrector methods for a linear stochastic oscillator with additive noise
Mathematical and Computer Modelling: An International Journal
A Multistage Wiener Chaos Expansion Method for Stochastic Advection-Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
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Stochastic Hamiltonian systems with multiplicative noise, phase flows of which preserve symplectic structure, are considered. To construct symplectic methods for such systems, sufficiently general fully implicit schemes, i.e., schemes with implicitness both in deterministic and stochastic terms, are needed. A new class of fully implicit methods for stochastic systems is proposed. Increments of Wiener processes in these fully implicit schemes are substituted by some truncated random variables. A number of symplectic integrators is constructed. Special attention is paid to systems with separable Hamiltonians. Some results of numerical experiments are presented. They demonstrate superiority of the proposed symplectic methods over very long times in comparison with nonsymplectic ones.