Chebyshev rational spectral method for long-short wave equations

We consider the initial boundary value problem of the long-short wave equations on the whole line. A fully discrete spectral approximation scheme is developed based on Chebyshev rational functions in space and central difference in time. A priori estimates are derived which are crucial to study numerical stability and convergence of the fully discrete scheme. Then, unconditional numerical stability is proved. Convergence of the fully discrete scheme is shown by the method of error estimates. Finally, numerical experiments are presented to demonstrate the efficiency and accuracy of the convergence results.