Adaptive stepsize based on control theory for stochastic differential equations

DOI10.1016/j.cam.2004.01.027zbMath1049.65009OpenAlexW1981312473MaRDI QIDQ596212

Kevin Burrage, R. Herdiana, Pamela M. Burrage

Publication date: 10 August 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.01.027

zbMATH Keywords

stabilityPredictive controlstiff systemsdigital filterproportional integral controlStochastic differential equationsStochastic Runge-Kutta methodsVariable stepsize

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Numerical methods for initial value problems involving ordinary differential equations (65L05) 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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (17)

Stabilized explicit Runge-Kutta methods for multi-asset American options ⋮ Adaptive time-stepping using control theory for the chemical Langevin equation ⋮ A Review of Stochastic and Delay Simulation Approaches in Both Time and Space in Computational Cell Biology ⋮ SDELab: A package for solving stochastic differential equations in MATLAB ⋮ Weak variable step-size schemes for stochastic differential equations based on controlling conditional moments ⋮ Strong convergence of an adaptive time-stepping Milstein method for SDEs with monotone coefficients ⋮ A Variable Step Size Riemannian Sum for an Itô Integral ⋮ Unnamed Item ⋮ Stochastic simulation of chemical reactions in spatially complex media ⋮ Long-term adaptive symplectic numerical integration of linear stochastic oscillators driven by additive white noise ⋮ Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients ⋮ SERK2v2: A new second‐order stabilized explicit Runge‐Kutta method for stiff problems ⋮ Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations ⋮ A stepsize control algorithm for SDEs with small noise based on stochastic Runge-Kutta Maruyama methods ⋮ Second-order stabilized explicit Runge-Kutta methods for stiff problems ⋮ The fully implicit stochastic-\(\alpha \) method for stiff stochastic differential equations ⋮ Adaptive time-stepping for the strong numerical solution of stochastic differential equations

Cites Work

• Unnamed Item
• High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula
• A PI stepsize control for the numerical solution of ordinary differential equations
• Step size control in the numerical solution of stochastic differential equations
• Control Strategies for the Iterative Solution of Nonlinear Equations in ODE Solvers
• Solving Ordinary Differential Equations I
• Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
• Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
• Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations
• Balanced Implicit Methods for Stiff Stochastic Systems
• Robust Defect Control with Runge–Kutta Schemes
• A Variable Stepsize Implementation for Stochastic Differential Equations
• Adaptive weak approximation of stochastic differential equations
• Digital filters in adaptive time-stepping

This page was built for publication: Adaptive stepsize based on control theory for stochastic differential equations