| Abstract: |
| For the one-dimensional stochastic Gross-Pitaevskii equation, we propose a fully discrete finite difference scheme based on operator splitting, and establish that the scheme attains a strong convergence order of $O(\tau^2+h^2)$, where $\tau$ and $h$ denote the temporal and spatial step sizes, respectively. First, under suitable assumptions, we analyze the regularity of both the exact solution and the splitting solution. Subsequently, we employ the Crank-Nicolson scheme for temporal discretization and the finite difference method for spatial discretization, and establish the convergence theory of the fully discrete scheme under the condition $h^2$ |
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