Weak Second Order Explicit Exponential Runge--Kutta Methods for Stochastic Differential Equations

DOI10.1137/15M1041341zbMath1387.65064WikidataQ115525644 ScholiaQ115525644MaRDI QIDQ4597615

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Publication date: 13 December 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

stiffnesssplitting methodItô stochastic differential equationexplicit methodnoncommutative noiseexponential integrator

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (13)

Drift-preserving numerical integrators for stochastic Poisson systems ⋮ A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations ⋮ Integration of the stochastic underdamped harmonic oscillator by the \(\theta \)-method ⋮ Split S-ROCK methods for high-dimensional stochastic differential equations ⋮ Analytical and numerical investigation of stochastic differential equations with applications using an exponential Euler-Maruyama approach ⋮ The Truncated Em Method for Jump-Diffusion Sddes with Super-Linearly Growing Diffusion and Jump Coefficients ⋮ Structure-preserving stochastic conformal exponential integrator for linearly damped stochastic differential equations ⋮ Runge-Kutta Lawson schemes for stochastic differential equations ⋮ Modified Strang splitting for semilinear parabolic problems ⋮ Strong convergence of a GBM based tamed integrator for SDEs and an adaptive implementation ⋮ Tamed Runge-Kutta methods for SDEs with super-linearly growing drift and diffusion coefficients ⋮ Exponential integrators for stochastic Maxwell's equations driven by Itô noise ⋮ A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations

Uses Software

• MersenneTwister
• S-ROCK

Cites Work

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• Mean-square stability analysis of numerical schemes for stochastic differential systems
• Weak second order S-ROCK methods for Stratonovich stochastic differential equations
• Convergence analysis of trigonometric methods for stiff second-order stochastic differential equations
• A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems
• A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems
• Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation
• The convergence and MS stability of exponential Euler method for semilinear stochastic differential equations
• On preserving long-time features of a linear stochastic oscillator
• Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
• S-ROCK methods for stiff Itô SDEs
• \(A\)-stability and stochastic mean-square stability
• Strong first order \(S\)-ROCK methods for stochastic differential equations
• Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations
• Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
• Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
• Exponential integrators
• Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
• Splitting methods
• S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
• Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
• Weak Approximation of Solutions of Systems of Stochastic Differential Equations
• On the Internal Stability of Explicit,m-Stage Runge-Kutta Methods for Largem-Values
• Generalized Runge-Kutta Processes for Stiff Initial-value Problems†
• Mersenne twister
• Exponential Integrators for Large Systems of Differential Equations
• Stochastic burgers equation with correlated noise
• Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
• Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 1: Dirichlet Boundary Conditions
• On the Construction and Comparison of Difference Schemes
• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
• An exponential method of numerical integration of ordinary differential equations
• Second order Chebyshev methods based on orthogonal polynomials

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