A Legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations

In this study, a Legendre spectral tau method is revisited to handle the multi-term time-fractional diffusion equations (MTT-FDEs). An error estimate and rigorous convergence analysis are carried out using some critical theorems. The applicability and accuracy of the solution method are demonstrated by a numerical example to verify the theoretical analysis.