Abstract
We develop efficient algorithms based on the Legendre-tau approximation for one- and two-dimensional fractional Rayleigh–Stokes problems for a generalized second-grade fluid. The time fractional derivative is described in the Riemann–Liouville sense. Discussions on the L2-convergence of the proposed method are presented. Numerical results for one- and two-dimensional examples with smooth and nonsmooth solutions are provided to verify the validity of the theoretical analysis, and to illustrate the efficiency of the proposed algorithms.
•Two efficient algorithms for the multi-dimensional fractional Rayleigh–Stokes problem are proposed.•The proposed algorithms are based on the Legendre spectral tau method.•Discussions on the L2-convergence of the method are presented.•The theoretical results are verified by numerical experiments.