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A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation (1902.07925v2)
Published 21 Feb 2019 in math.NA and cs.NA
Abstract: We propose a Fourier pseudo-spectral scheme for the space-fractional nonlinear Schr\"odinger equation. The proposed scheme has the following features: it is linearly implicit, it preserves two invariants of the equation, its unique solvability is guaranteed without any restrictions on space and time step sizes. The scheme requires solving a complex symmetric linear system per time step. To solve the system efficiently, we also present a certain variable transformation and preconditioner.