We consider the initial-boundary-value problem for a homogeneous time fractional diffusion equation with an initial condition $u_0(x)$ and a homogeneous Dirichlet boundary condition in a bounded interval $[0,L]$. We study a semidiscrete approximation scheme, the pseudo-spectral method, using the characteristic Lagrange polynomials for this problem. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the proposed method.
