Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

DOI10.1016/S0010-4655(01)00324-1zbMath0991.65005MaRDI QIDQ5956335

Tianhai Tian, Kevin Burrage

Publication date: 1 September 2002

Published in: Computer Physics Communications (Search for Journal in Brave)

zbMATH Keywords

stabilitynumerical resultsRunge-Kutta methodssplitting techniquesstiff accuracyStratonovich 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) 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 (10)

An error corrected Euler-Maruyama method for stiff stochastic differential equations ⋮ Split-step forward methods for stochastic differential equations ⋮ Second-order balanced stochastic Runge-Kutta methods with multi-dimensional studies ⋮ High order local linearization methods: an approach for constructing A-stable explicit schemes for stochastic differential equations with additive noise ⋮ A class of weak second order split-drift stochastic Runge-Kutta schemes for stiff SDE systems ⋮ Analysis of Multiscale Integrators for Multiple Attractors and Irreversible Langevin Samplers ⋮ On the stability of some second order numerical methods for weak approximation of Itô SDEs ⋮ Split-step backward balanced Milstein methods for stiff stochastic systems ⋮ An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gases ⋮ Asymptotic mean-square stability of weak second-order balanced stochastic Runge-Kutta methods for multi-dimensional Itô stochastic differential systems

Cites Work

• Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations
• Computer simulations of multiplicative stochastic differential equations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems
• Robust algorithms for solving stochastic partial differential equations
• Stochastic methods for ill-posed problems
• Two-stage stochastic Runge-Kutta methods for stochastic differential equations
• Order Conditions of Stochastic Runge--Kutta Methods by B-Series
• Numerical Treatment of Stochastic Differential Equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Balanced Implicit Methods for Stiff Stochastic Systems
• Predictor-Corrector Methods of Runge--Kutta Type for Stochastic Differential Equations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• The composite Euler method for stiff stochastic differential equations
• High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

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