Convergence of a split-step Hermite method for the Gross-Pitaevskii equation

摘要

An error analysis is given for a discretization of the Gross-Pitaevskii equation by Strang splitting in time and Hermite collocation in space. A second-order error bound in L~2 for the semidiscretization error of the Strang splitting in time is proven under suitable regularity assumptions on the exact solution. For the semidiscretization in space, high-order convergence is shown, depending on the regularity of the exact solution. The analyses of the semidiscretizations in time and space are finally combined into an error analysis of the fully discrete method.