Exponential Integrators for Stochastic Maxwell's Equations Driven by Itô Noise

Abstract

This article presents explicit exponential integrators for stochastic Maxwell's equations driven by both multiplicative and additive noises. By utilizing the regularity estimate of the mild solution, we first prove that the strong order of the numerical approximation is $\frac{1}{2}$ for general multiplicative noise. Combing a proper decomposition with the stochastic Fubini's theorem, the strong order of the proposed scheme is shown to be $1$ for additive noise. Moreover, for linear stochastic Maxwell's equation with additive noise, the proposed time integrator is shown to preserve exactly the symplectic structure, the evolution of the energy as well as the evolution of the divergence in the sense of expectation. Several numerical experiments are presented in order to verify our theoretical findings.

arXiv comment21 Pages

References in corpus (5)

• A trigonometric method for the linear stochastic wave equation
• An exponential integrator scheme for time discretization of nonlinear stochastic wave equation
• An accelerated exponential time integrator for semi-linear stochastic strongly damped wave equation with additive noise
• Propagation of ultra-short solitons in stochastic Maxwell's equations
• Mean-square convergence of a semi-discrete scheme for stochastic nonlinear Maxwell equations

Cited by in corpus (8)

• Drift-preserving numerical integrators for stochastic Hamiltonian systems
• Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise
• Drift-preserving numerical integrators for stochastic Poisson systems
• A symplectic discontinuous Galerkin full discretization for stochastic Maxwell equations
• Temporal approximation of stochastic evolution equations with irregular nonlinearities
• Pathwise Uniform Convergence of Time Discretisation Schemes for SPDEs
• A new efficient operator splitting method for stochastic Maxwell equations
• Weak intermittency and second moment bound of a fully discrete scheme for stochastic heat equation