Integration of the stochastic underdamped harmonic oscillator by the \(\theta \)-method

DOI10.1016/j.matcom.2022.03.012OpenAlexW4220724241WikidataQ113869160 ScholiaQ113869160MaRDI QIDQ2672362

Yanyan Li

Publication date: 8 June 2022

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2022.03.012

zbMATH Keywords

numerical integrationnumerical methodsstochastic differential equationsstochastic theta methodssecond order momentstochastic underdamped oscillator

Mathematics Subject Classification ID

Quantum theory (81-XX) Statistical mechanics, structure of matter (82-XX)

Uses Software

• S-ROCK

Cites Work

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• On the numerical discretisation of stochastic oscillators
• A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems
• Locally linearized methods for the simulation of stochastic oscillators driven by random forces
• On preserving long-time features of a linear stochastic oscillator
• A survey of numerical methods for stochastic differential equations
• Stochastic oscillators
• Numerical preservation of long-term dynamics by stochastic two-step methods
• Numerical simulation of a linear stochastic oscillator with additive noise
• Runge-Kutta Lawson schemes for stochastic differential equations
• On the numerical structure preservation of nonlinear damped stochastic oscillators
• Long-term analysis of stochastic \(\theta\)-methods for damped stochastic oscillators
• A review on numerical schemes for solving a linear stochastic oscillator
• Two-step strong order 1.5 schemes for stochastic differential equations
• Predictor-corrector methods for a linear stochastic oscillator with additive noise
• Stochastic Dynamics and Irreversibility
• An Introduction to Mechanics
• S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
• Preservation of probabilistic laws through Euler methods for ornstein-uhlenbeck process
• The Invariance of Asymptotic Laws of Linear Stochastic Systems under Discretization
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Symplectic Integration of Hamiltonian Systems with Additive Noise
• Weak Second Order Explicit Exponential Runge--Kutta Methods for Stochastic Differential Equations
• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Weak Second Order Conditions for Stochastic Runge--Kutta Methods
• Stochastic Oscillator: Brownian Motion with Adhesion
• Runge–Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations
• Numerical Methods for Second‐Order Stochastic Differential Equations
• On the Theory of the Brownian Motion II

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