Mean-square convergence of a semi-discrete scheme for stochastic nonlinear Maxwell equations
It provides a numerical method with proven convergence for stochastic Maxwell equations, which is important for computational electromagnetics under uncertainty.
The paper proposes a semi-implicit Euler scheme for stochastic nonlinear Maxwell equations with multiplicative Ito noise, achieving mean-square convergence of order 1/2.
In this paper, we propose a semi-implicit Euler scheme to discretize the stochastic nonlinear Maxwell equations with multiplicative Ito noise, which is implicit in the drift term and explicit in the diffusion term of the equations, in order to suited to Ito product. Uniform bounds with high regularities of solutions for both the continuous and the discrete problems are obtained, which are crucial properties to derive the mean-square convergence with certain order. Allowing sufficient spatial regularity and utilizing the energy estimate technique, the convergence order 1/2 in mean-square sense is obtained.