Numerical method for the zero dispersion limit of the fractional
Korteweg-de Vries equation
Numerical method for the zero dispersion limit of the fractional
Korteweg-de Vries equation
We present a fully discrete Crank-Nicolson Fourier-spectral-Galerkin (FSG) scheme for approximating solutions of the fractional Korteweg-de Vries (KdV) equation, which involves a fractional Laplacian with exponent $\alpha \in [1,2]$ and a small dispersion coefficient of order $\varepsilon^2$. The solution in the limit as $\varepsilon \to 0$ is known as the …