Stochastic Conformal Integrators for Linearly Damped Stochastic Poisson Systems

Area of Science:

• Numerical Analysis
• Stochastic Systems
• Mathematical Physics

Background:

• Stochastic Poisson systems are crucial in modeling complex phenomena.
• Existing numerical methods may struggle with stability and accuracy for damped systems.
• Conformal integrators offer a promising approach for preserving system properties.

Purpose of the Study:

• To propose and analyze conformal integrators for linearly damped stochastic Poisson systems.
• To investigate the qualitative and quantitative properties of these novel numerical integrators.
• To demonstrate the efficacy of the proposed methods through numerical experiments.

Main Methods:

• Development of conformal integrators tailored for linearly damped stochastic Poisson systems.
• Analysis of properties including Casimir and Hamiltonian function preservation.
• Derivation of almost sure bounds and strong/weak convergence rates.

Main Results:

• The proposed conformal integrators preserve key dynamical properties.
• Established theoretical bounds and convergence rates for the numerical solutions.
• Numerical experiments confirmed the theoretical findings on benchmark systems.

Conclusions:

• Conformal integrators provide a robust and accurate numerical framework for linearly damped stochastic Poisson systems.
• The study offers a significant advancement in the numerical simulation of stochastic dynamical systems.
• The validated methods have broad applicability in physics and related fields.