A high-order discontinuous Galerkin method for Itô stochastic ordinary differential equations

DOI10.1016/j.cam.2016.05.034zbMath1345.60066OpenAlexW2414734641MaRDI QIDQ738961

D. Kharzeev

Publication date: 16 August 2016

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.2016.05.034

zbMATH Keywords

A-stabilitydiscontinuous Galerkin methodmean-square convergenceconvergence orderWong-Zakai approximationItō stochastic differential equation

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (9)

Application of operational matrices for solving system of linear Stratonovich Volterra integral equation ⋮ An Efficient Finite Difference Method for Stochastic Linear Second-Order Boundary-Value Problems Driven by Additive White Noises ⋮ A discontinuous Galerkin method for systems of stochastic differential equations with applications to population biology, finance, and physics ⋮ The discontinuous Galerkin method for general nonlinear third-order ordinary differential equations ⋮ A stochastic local discontinuous Galerkin method for stochastic two-point boundary-value problems driven by additive noises ⋮ A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations ⋮ The discontinuous Galerkin method for stochastic differential equations driven by additive noises ⋮ Exponential mean-square stability of numerical solutions for stochastic delay integro-differential equations with Poisson jump ⋮ Unnamed Item

Uses Software

• RODAS
• Mulprec
• sde

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Evaluation of conditional Wiener integrals by numerical integration of stochastic differential equations
• Optimal global approximation of SDEs with time-irregular coefficients in asymptotic setting
• A discontinuous Galerkin method for higher-order ordinary differential equations
• Superconvergence of rectangular finite element with interpolated coefficients for semilinear elliptic problem
• \(A\)-stability of Runge-Kutta methods for systems with additive noise
• A class of approximations of Brownian motion
• A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
• Optimal pointwise approximation of SDEs based on Brownian motion at discrete points
• The optimal uniform approximation of systems of stochastic differential equations
• Weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with non-regular drift
• Minimal asymptotic error for one-point approximation of SDEs with time-irregular coefficients
• On the relation between ordinary and stochastic differential equations
• Strong approximation of solutions of stochastic differential equations with time-irregular coefficients via randomized Euler algorithm
• Simulation and inference for stochastic differential equations. With R examples.
• A random Euler scheme for Carathéodory differential equations
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• Numerical Methods in Scientific Computing, Volume I
• Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
• A Method of Second-Order Accuracy Integration of Stochastic Differential Equations
• Discontinuous Galerkin Methods for Ordinary Differential Equations
• Numerical Treatment of Stochastic Differential Equations
• Approximate Integration of Stochastic Differential Equations
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Superconvergence of Discontinuous Galerkin Methods for Scalar Nonlinear Conservation Laws in One Space Dimension
• Optimal approximation of stochastic differential equations by adaptive step-size control
• Solving Ordinary Differential Equations II
• Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments
• On the Convergence of Ordinary Integrals to Stochastic Integrals
• A class ofA-stable methods
• A special stability problem for linear multistep methods
• The optimal discretization of stochastic differential equations
• High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

This page was built for publication: A high-order discontinuous Galerkin method for Itô stochastic ordinary differential equations