A numerical study for the KdV and the good Boussinesq equations using Fourier Chebyshev tau meshless method

The current paper presents a scheme, which combines Fourier spectral method and Chebyshev tau meshless method based on the highest derivative (CTMMHD) to solve the nonlinear KdV equation and the good Boussinesq equation. Fourier spectral method is used to approximate the spatial variable, and the problem is converted to a series of equations with Fourier coefficients as unknowns. Then, CTMMHD is applied blockwise in time direction. For the long time computing of solitons, we introduce the computational area moving technique. The numerical results show that the accuracy of Fourier-CTMMHD is good and the computational area moving technique makes the long-time numerical behavior well for the problems with solitons moving towards the same direction.

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