A-stability preserving perturbation of Runge-Kutta methods for stochastic differential equations

DOI10.1016/j.aml.2019.106098OpenAlexW2981852941MaRDI QIDQ2184909

Raffaele D'Ambrosio, Vincenzo Citro, Stefano Di Giovacchino

Publication date: 2 June 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2019.106098

zbMATH Keywords

stochastic differential equationsstochastic Runge-Kutta methodsmean-square a-stability

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (7)

Dynamical low-rank approximation to the solution of parabolic differential equations ⋮ Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems ⋮ How do Monte Carlo estimates affect stochastic geometric numerical integration? ⋮ Nonlinear stability issues for stochastic Runge-Kutta methods ⋮ On the numerical structure preservation of nonlinear damped stochastic oscillators ⋮ Perturbative analysis of stochastic Hamiltonian problems under time discretizations ⋮ Two-step Runge-Kutta methods for stochastic differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations
• Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise
• Economical Runge-Kutta methods for numerical solution of stochastic differential equations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• On the stability of \(\vartheta\)-methods for stochastic Volterra integral equations
• Numerical preservation of long-term dynamics by stochastic two-step methods
• Implicit stochastic Runge-Kutta methods for stochastic differential equations
• Drift-preserving numerical integrators for stochastic Hamiltonian systems
• Exponential mean-square stability properties of stochastic linear multistep methods
• Stability issues for selected stochastic evolutionary problems: a review
• Order conditions for stochastic Runge-Kutta methods preserving quadratic invariants of Stratonovich SDEs
• Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise
• Runge-Kutta methods for Itô stochastic differential equations with scalar noise
• A spectral method for stochastic fractional differential equations
• Order Conditions of Stochastic Runge--Kutta Methods by B-Series
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Stochastic Runge–Kutta Methods for Itô SODEs with Small Noise
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• B–Series Analysis of Stochastic Runge–Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values
• Runge–Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations

This page was built for publication: A-stability preserving perturbation of Runge-Kutta methods for stochastic differential equations