Predictor–corrector methods for a linear stochastic oscillator with additive noise

The predictor–corrector methods P(EC)kP(EC)k with equidistant discretization are applied to the numerical integration of a linear stochastic oscillator. Their ability in preserving the symplecticity, the linear growth property of the second moment, and the oscillation property of the solution of this stochastic system is studied. Their mean-square orders of convergence are discussed. Numerical experiments are performed.