The authors study different finite difference schemes for solving the generalized nonlinear Schrödinger (GNLS) equation
A new linearized Crank-Nicolson-type scheme is presented by applying an extrapolation technique to the real coefficients of the nonlinear terms in the GNLS equations.
Three particular model situations with
are studied. The authors present results of numerical experiments, where the proposed scheme is compared with other Crank-Nicolson-type schemes, Hopscotch-type schemes, split step Fourier schemes, and with spectral schemes. The numerical experiments presented at the end of the paper demonstrate the efficiency and robustness of the proposed linearized Crank-Nicolson scheme for solving GNLS equations.