Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

DOI10.1007/s10543-012-0372-6zbMath1259.65002OpenAlexW2088114342MaRDI QIDQ1759582

Kevin Burrage, Jamie Alcock

Publication date: 21 November 2012

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://eprints.qut.edu.au/53878/1/KEVIN_milbal1.pdf

zbMATH Keywords

stabilityconvergenceerror boundsbalanced methodMilstein methodstiff Itô stochastic differential equations

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) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for stiff equations (65L04)

Related Items (8)

Approximating explicitly the mean-reverting CEV process ⋮ First-order weak balanced schemes for stochastic differential equations ⋮ Convergence and stability of two classes of theta-Milstein schemes for stochastic differential equations ⋮ Balanced implicit methods with strong order 1.5 for solving stochastic differential equations ⋮ Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations ⋮ Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs ⋮ A Stable Numerical Scheme for Stochastic Differential Equations with Multiplicative Noise ⋮ A class of balanced stochastic Runge-Kutta methods for stiff SDE systems

Uses Software

• RODAS
• S-ROCK

Cites Work

• A note on the balanced method
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Implicit stochastic Runge-Kutta methods for stochastic differential equations
• S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
• Balanced Implicit Methods for Stiff Stochastic Systems
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Balanced Milstein Methods for Ordinary SDEs
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