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Additive Noise

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Jialin Hong – 1st expert on this subject based on the ideXlab platform

  • Runge–Kutta Semidiscretizations for Stochastic Maxwell Equations with Additive Noise
    SIAM Journal on Numerical Analysis, 2019
    Co-Authors: Chuchu Chen, Jialin Hong, Lihai Ji

    Abstract:

    The paper concerns semidiscretizations in time of stochastic Maxwell equations driven by Additive Noise. We show that the equations admit physical properties and mathematical structures, including …

  • Runge-Kutta semidiscretizations for stochastic Maxwell equations with Additive Noise
    arXiv: Numerical Analysis, 2018
    Co-Authors: Chuchu Chen, Jialin Hong, Lihai Ji

    Abstract:

    The paper concerns semidiscretizations in time of stochastic Maxwell equations driven by Additive Noise. We show that the equations admit physical properties and mathematical structures, including regularity, energy and divergence evolution laws, and stochastic symplecticity, etc. In order to inherit the intrinsic properties of the original system, we introduce a general class of stochastic Runge-Kutta methods, and deduce the condition of symplecticity-preserving. By utilizing a priori estimates on numerical approximations and semigroup approach, we show that the methods, which are algebraically stable and coercive, are well-posed and convergent with order one in mean-square sense, which answers an open problem in [Chen and Hong, SIAM J. Numer. Anal., 2016] for stochastic Maxwell equations driven by Additive Noise.

  • Stochastic symplectic Runge–Kutta methods for the strong approximation of Hamiltonian systems with Additive Noise
    Journal of Computational and Applied Mathematics, 2017
    Co-Authors: Weien Zhou, Jialin Hong, Jingjing Zhang, Songhe Song

    Abstract:

    Abstract In this paper, we construct stochastic symplectic Runge–Kutta (SSRK) methods of high strong order for Hamiltonian systems with Additive Noise. By means of colored rooted tree theory, we combine conditions of mean-square order 1.5 and symplectic conditions to get totally derivative-free schemes. We also achieve mean-square order 2.0 symplectic schemes for a class of second-order Hamiltonian systems with Additive Noise by similar analysis. Finally, linear and non-linear systems are solved numerically, which verifies the theoretical analysis on convergence order. Especially for the stochastic harmonic oscillator with Additive Noise, the linear growth property can be preserved exactly over long-time simulation.

Liying Zhang – 2nd expert on this subject based on the ideXlab platform

  • a stochastic multi symplectic scheme for stochastic maxwell equations with Additive Noise
    Journal of Computational Physics, 2014
    Co-Authors: Jialin Hong, Lihai Ji, Liying Zhang

    Abstract:

    Abstract In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with Additive Noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with Additive Noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.

  • A stochastic multi-symplectic scheme for stochastic Maxwell equations with Additive Noise
    Journal of Computational Physics, 2014
    Co-Authors: Jialin Hong, Lihai Ji, Liying Zhang

    Abstract:

    Abstract In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with Additive Noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with Additive Noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.

Lihai Ji – 3rd expert on this subject based on the ideXlab platform

  • Runge–Kutta Semidiscretizations for Stochastic Maxwell Equations with Additive Noise
    SIAM Journal on Numerical Analysis, 2019
    Co-Authors: Chuchu Chen, Jialin Hong, Lihai Ji

    Abstract:

    The paper concerns semidiscretizations in time of stochastic Maxwell equations driven by Additive Noise. We show that the equations admit physical properties and mathematical structures, including …

  • Runge-Kutta semidiscretizations for stochastic Maxwell equations with Additive Noise
    arXiv: Numerical Analysis, 2018
    Co-Authors: Chuchu Chen, Jialin Hong, Lihai Ji

    Abstract:

    The paper concerns semidiscretizations in time of stochastic Maxwell equations driven by Additive Noise. We show that the equations admit physical properties and mathematical structures, including regularity, energy and divergence evolution laws, and stochastic symplecticity, etc. In order to inherit the intrinsic properties of the original system, we introduce a general class of stochastic Runge-Kutta methods, and deduce the condition of symplecticity-preserving. By utilizing a priori estimates on numerical approximations and semigroup approach, we show that the methods, which are algebraically stable and coercive, are well-posed and convergent with order one in mean-square sense, which answers an open problem in [Chen and Hong, SIAM J. Numer. Anal., 2016] for stochastic Maxwell equations driven by Additive Noise.

  • a stochastic multi symplectic scheme for stochastic maxwell equations with Additive Noise
    Journal of Computational Physics, 2014
    Co-Authors: Jialin Hong, Lihai Ji, Liying Zhang

    Abstract:

    Abstract In this paper we investigate a stochastic multi-symplectic method for stochastic Maxwell equations with Additive Noise. Based on the stochastic version of variational principle, we find a way to obtain the stochastic multi-symplectic structure of three-dimensional (3-D) stochastic Maxwell equations with Additive Noise. We propose a stochastic multi-symplectic scheme and show that it preserves the stochastic multi-symplectic conservation law and the local and global stochastic energy dissipative properties, which the equations themselves possess. Numerical experiments are performed to verify the numerical behaviors of the stochastic multi-symplectic scheme.