Abstract
A semi-linearized time-stepping method based on the finite difference in time and Fourier pseudospectral discretization for spatial derivatives is constructed and analyzed for the Klein–Gordon–Schrödinger equation. The resulting numerical scheme is proved to conserve the total mass and energy in the discrete levels. The maximum norm error estimates reflecting the second-order accuracy in time and spectral accuracy in space are established by using the standard energy method coupled with the induction argument. An efficient numerical algorithm is reported to speed up the evaluation of resulting algebra equation by means of the fast discrete Fourier transform. Numerical experiments are presented to show the effectiveness of our method and to confirm our analysis.
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