Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations

DOI10.1007/s10543-013-0419-3zbMath1276.65003OpenAlexW2084095385MaRDI QIDQ369398

Yoshio Komori, Evelyn Buckwar

Publication date: 24 September 2013

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-013-0419-3

zbMATH Keywords

numerical examplesItô stochastic differential equationexplicit methodmean square stabilitystochastic Runge-Kutta methodsweak second-order methods

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) 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)

Stochastic symplectic Runge-Kutta methods for the strong approximation of Hamiltonian systems with additive noise ⋮ High strong order stochastic Runge-Kutta methods for Stratonovich stochastic differential equations with scalar noise ⋮ A-stability preserving perturbation of Runge-Kutta methods for stochastic differential equations ⋮ Nonlinear stability issues for stochastic Runge-Kutta methods ⋮ The truncated Milstein method for stochastic differential equations with commutative noise ⋮ Efficient weak second-order stochastic Runge-Kutta methods for Itô stochastic differential equations ⋮ Asymptotic mean-square stability of weak second-order balanced stochastic Runge-Kutta methods for multi-dimensional Itô stochastic differential systems

Uses Software

• RODAS
• MersenneTwister

Cites Work

• Unnamed Item
• Unnamed Item
• Mean-square stability analysis of numerical schemes for stochastic differential systems
• A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems
• A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods
• Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations
• Stochastic stability of differential equations. With contributions by G. N. Milstein and M. B. Nevelson
• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
• Mean-square stability of numerical schemes for stochastic differential systems
• \(A\)-stability and stochastic mean-square stability
• Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations
• Second order Runge-Kutta methods for Stratonovich stochastic differential equations
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• Second Order Runge–Kutta Methods for Itô Stochastic Differential Equations
• Mersenne twister
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Weak Second Order Conditions for Stochastic Runge--Kutta Methods
• Stahle ROW-Type Weak Scheme for Stochastic Differential Equations
• Solving Ordinary Differential Equations II
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations

This page was built for publication: Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations