An improved tau method for the multi-dimensional fractional Rayleigh-Stokes problem for a heated generalized second grade fluid

作者：Zaky, Mahmoud A.^*

来源：Computers & Mathematics with Applications, 2018, 75(7): 2243-2258.

DOI：10.1016/j.camwa.2017.12.004

• Fractional Rayleigh-Stokes problem
• Riemann-Liouville fractional derivative
• Legendre-tau method
• Convergence analysis

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 L-2-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.

• 出版日期2018-4-1