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. For the numerical solution of the cubic nonlinear Schrödinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting scheme in time is considered. This scheme is shown to converge even for initial data with very low regularity. In particular, for data in \ (Hˢ (T²) \), where \ (s 0\), convergence of order \ (O (^s/2+N^-s) \) is proved in \ (L²\). Here \ (\) denotes the time step size and \ (N\) the number of Fourier modes considered. The proof of this result is carried out in an abstract framework of discrete Bourgain spaces; the final convergence result, however, is given in \ (L²\). The stated convergence behavior is illustrated by several numerical examples. Keywordsnonlinear Schrödinger equationlow regularityconvergence of full dicretizationLie splittingBourgain techniquesMSC codes65M1265M1535Q55
Ji et al. (Tue,) studied this question.