A note on an accelerated exponential Euler method for parabolic SPDEs with additive noise

DOI10.1016/j.aml.2015.02.001zbMath1321.65159OpenAlexW2043232439MaRDI QIDQ494235

Rui-sheng Qi, Xiao-Jie Wang

Publication date: 31 August 2015

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2015.02.001

zbMATH Keywords

strong convergenceadditive noisesemilinear stochastic partial differential equationsoptimal regularity resultsaccelerated exponential Euler scheme

Mathematics Subject Classification ID

PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (14)

Convergence and stability of exponential integrators for semi-linear stochastic variable delay integro-differential equations ⋮ Stochastic exponential integrators for a finite element discretisation of SPDEs with additive noise ⋮ An accelerated exponential time integrator for semi-linear stochastic strongly damped wave equation with additive noise ⋮ Strong convergence of a stochastic Rosenbrock-type scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise ⋮ Magnus-type integrator for non-autonomous SPDEs driven by multiplicative noise ⋮ A numerical method for a nonlocal diffusion equation with additive noise ⋮ An efficient explicit full-discrete scheme for strong approximation of stochastic Allen-Cahn equation ⋮ Optimal strong convergence rates of numerical methods for semilinear parabolic SPDE driven by Gaussian noise and Poisson random measure ⋮ Strong convergence analysis of the stochastic exponential Rosenbrock scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise ⋮ Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear SPDEs driven by multiplicative or additive noise ⋮ Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear non-autonomous SPDEs driven by multiplicative or additive noise ⋮ Pathwise convergence of an efficient scheme for SPDEs with non-globally Lipschitz nonlinearity ⋮ Mittag--Leffler Euler Integrator for a Stochastic Fractional Order Equation with Additive Noise ⋮ A modified semi-implicit Euler-Maruyama scheme for finite element discretization of SPDEs with additive noise

Cites Work

• Strong and weak approximation of semilinear stochastic evolution equations
• Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
• Efficient simulation of nonlinear parabolic SPDEs with additive noise
• Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space–time noise
• Stochastic exponential integrators for the finite element discretization of SPDEs for multiplicative and additive noise
• Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
• Galerkin Finite Element Methods for Stochastic Parabolic Partial Differential Equations
• Stochastic Equations in Infinite Dimensions

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