Abstract:

Fourier seimdiscrete and fully discrete schemes that inherit the conservation properties of differential equation is presented to numerically solve the nolinear SchrÖdinger equation with periodic boundary conditions. The conditions under which the fully discrete form has an unique solution are discussed and analyzied the error estimates. The implement of the fully discrete scheme requires the solution of a nonlinear system of equations at each time step. The theoretical results are corformed by the numberical experiments using the predictor-corrector algorithm.

Key words: nonlinear SchrÖdinger equation; Fourier spectral method; energy conservation; error estimate; predictor-corrector algorithm