A SECOND-ORDER EMBEDDED LOW-REGULARITY INTEGRATOR FOR THE QUADRATIC NONLINEAR SCHRODINGER EQUATION ON TORUS

摘要

A new embedded low-regularity integrator is proposed for the quadratic nonlinear Schrodinger equation on the one-dimensional torus. Second-order convergence in H-gamma is proved for solutions in C([0, T]; H-gamma) with gamma > 3/2, i.e., no additional regularity in the solution is required. The proposed method is fully explicit and can be computed by the fast Fourier transform with O(N log N) operations at every time level, where N denotes the degrees of freedom in the spatial discretization. The method extends the first-order convergent low-regularity integrator in [14] to second-order time discretization in the case gamma > 3/2 without requiring additional regularity of the solution. Numerical experiments are presented to support the theoretical analysis by illustrating the convergence of the proposed method.

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