Physical properties preserving numerical simulation of stochastic fractional nonlinear wave equation

Abstract

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.