Physical properties preserving numerical simulation of stochastic fractional nonlinear wave equation.

• The energy of the stochastic space-fractional nonlinear wave equation is obtained under the two different noise case. • We use Crank-Nicolson difference method based on second-order fractional differences to simulate the different behavior of stochastic space-fractional nonlinear wave equation in additive noise and multiplicative noise. • The discrete averaged energy of the stochastic space-fractional nonlinear wave equation coincides with theoretical results. • The energy of system possesses dissipation-preserving or energy-conserving property under the suitable conditions. • The space-time convergence order of our numerical schemes in time and space is presented in the sense of expectation. In this paper, we numerically solve a stochastic space-fractional nonlinear wave equation which includes fractional derivative, nonlinear term, damping term and noise term. The energy of system in the continuous case is derived in detail and discrete energy preserving physical characteristic is also proved. We propose a numerical method that uses Crank-Nicolson difference discretization based on second-order fractional differences. The numerical schemes for stochastic space-fractional nonlinear wave equation with two different noise possess dissipation-preserving energy or energy-conserving under suitable conditions. Moreover, the convergence order of our numerical schemes in time and space is presented in the sense of expectation. Numerical experiments with various types of noise demonstrate that the dissipative property or conservative property coincides with theoretical results. [ABSTRACT FROM AUTHOR]