A comparison of the spectral and the discrete singular convolution schemes for the KdV-type equations

The discrete singular convolution (DSC) algorithm is applied to the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations with a particular emphasis on a comparison with the Fourier pseudospectral (FPS) method. The errors of the DSC algorithm with respect to the numerical resolution are investigated by using the discrete Fourier analysis. The numerical results indicate that the DSC method can be more accurate than the FPS method for many nonlinear wave problems that are non-bandlimited in nature.