Parameter Estimation for Stochastic Korteweg–de Vries Equations

In this paper, we propose two methods for parameter estimation in stochastic Korteweg–de Vries (KdV) equations with unknown parameters. Both methods are based on the numerical discretization of the stochastic KdV equation. Moreover, we further propose an extrapolation-based approach to improve the accuracy of parameter estimation. In addition, for the deterministic case, the convergence and conservation of the fully discrete schemes are analyzed. Both our theoretical analysis and numerical tests indicate the efficiency of the proposed methods for the KdV equations considered.