Spectral method for solving the time fractional Boussinesq equation

In this paper, Fourier spectral approximation for the time fractional Boussinesq equation with periodic boundary condition is considered. The space is discretized by the Fourier spectral method and the Crank-Nicolson scheme is used to discretize the Caputo time fractional derivative. Stability and convergence analysis of the numerical method are proven. Some numerical examples are included to testify the effectiveness of our given method. Based on the presented numerical results, the Fourier spectral method is shown to be effective for solving the time fractional Boussinesq equation.