An efficient high order numerical method is presented to solve the mobileimmobile
advection-dispersion model with the Coimbra time variable-order fractional
derivative, which is used to simulate solute transport in watershed catchments and
rivers. On establishing an efficient recursive algorithm based on the properties of Jacobi
polynomials to approximate the Coimbra variable-order fractional derivative operator,
we use spectral collocation method with both temporal and spatial discretisation
to solve the time variable-order fractional mobile-immobile advection-dispersion model.
Numerical examples then illustrate the effectiveness and high order convergence of our