Abstract
In this paper, a conservative compact finite difference scheme is presented for solving the N-coupled nonlinear Schrödinger–Boussinesq equations. By using the discrete energy method, it is proved that our scheme is unconditionally convergent in the maximum norm and the convergent rate is at O(τ2+h4) with time step τ and mesh size h. Numerical results including the comparisons with other numerical methods are reported to demonstrate the accuracy and efficiency of the method and to confirm our theoretical analysis.
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