An unconditionally stable compact ADI method for three-dimensional time-fractional convection–diffusion equation

A high-order compact finite difference method is presented for solving the three-dimensional (3D) time-fractional convection–diffusion equation (of order α∈(1,2)α∈(1,2)). The original equation is first transformed to a fractional diffusion-wave equation, then using fourth-order Padé approximation for spatial derivatives and the center difference method for time derivative respectively, a fully discrete implicit compact scheme is obtained. Furthermore, based on different splitting terms, three unconditionally stable ADI compact schemes with optimal convergence order are developed respectively. The resulting schemes in each ADI solution step corresponding to a strictly diagonally dominant matrix equation can be solved using the 1D tridiagonal Thomas algorithm with a considerable saving in computing time. Numerical experiments show that these schemes can significantly improve the time accuracy.