Numerical simulations for stochastic differential equations on manifolds by stochastic symmetric projection method

Wang, Zhenyu; Wang, Chenke; Ma, Qiang; Ding, Xiaohua

doi:10.1016/j.physa.2019.123305

Cited by 3 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to Theorems 2.1 and (2.1), the choice of S i is not unique, so that we can obtain better numerical integrators by adding appropriate homogeneous solutions. Besides, if the discrete gradient ∇I(x ′ , x) is symmetric, the corresponding numerical method is also symmetric [31].…”

Section: A Stochastic Discrete Gradient Methodsmentioning

confidence: 99%

Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods

Wang¹,

Ma²,

Ding³

2022

EAJAM

Self Cite

View full text Add to dashboard Cite

The deterministic discrete gradient method for stochastic differential equations is extended to equations with multiple conserved quantities. The equations with multiple conserved quantities in the Stratonovich sense are written in the skew-gradient form, which is used in the construction of the stochastic discrete gradient method. It is shown that the stochastic discrete gradient method has the mean-square convergence order one and preserves all conserved quantities. Besides, for a given skew-gradient form, the stochastic discrete gradient method is equivalent to the stochastic projection method. Numerical examples confirm the theoretical results and show the effectiveness of the method.

show abstract

Section: A Stochastic Discrete Gradient Methodsmentioning

confidence: 99%

Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods

Wang¹,

Ma²,

Ding³

2022

EAJAM

Self Cite

View full text Add to dashboard Cite

show abstract

Analysis on Characteristics of Customer Satisfaction to Gymnasiums Based on the Holographic Projection Technology

Yan

2022

Lecture Notes in Electrical Engineering

View full text Add to dashboard Cite

Forty years: Geometric numerical integration of dynamical systems in China

Huang,

Liu,

Tang

et al. 2024

Int. J. Model. Simul. Sci. Comput.

View full text Add to dashboard Cite

Kang Feng proposed the symplectic geometric algorithms for Hamiltonian systems at Beijing “International Symposium on Differential Geometry and Differential Equations” in August 1984, opening up a new field of research. Over the past 40 years, geometric numerical integration for dynamical systems has been irreplaceably applied in numerous fields, including celestial mechanics, plasma physics, fluid mechanics, biochemistry, meteorological forecasting, seismic exploration, data science and artificial intelligence. This paper mainly summarizes the achievements of geometric numerical integration for dynamical systems in China over the past 40 years.

show abstract

Numerical simulations for stochastic differential equations on manifolds by stochastic symmetric projection method

Cited by 3 publications

References 16 publications

Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods

Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods

Analysis on Characteristics of Customer Satisfaction to Gymnasiums Based on the Holographic Projection Technology

Forty years: Geometric numerical integration of dynamical systems in China

Contact Info

Product

Resources

About