A Chebyshev pseudo-spectral method for the multi-dimensional fractional Rayleigh problem for a generalized Maxwell fluid with Robin boundary conditions

Abstract

Many pseudospectral schemes have been developed for time fractional partial differential equations, most of which use the spectral tau method. In this study, we develop an accurate numerical scheme using a combination of Lagrange and Chebyshev polynomials of the first kind for the multi-dimensional fractional Rayleigh problem integrated using the Gauss–Lobatto quadrature. The Chebyshev expansion coefficients are evaluated using the orthogonality condition of the polynomials. Arbitrary temporal derivatives are approximated using shifted Chebyshev polynomials, while the spatial derivatives are approximated using Lagrange basis functions. To establish the accuracy of the proposed scheme, we present a convergence analysis of the absolute errors. The convergence analysis shows that the absolute error tends to zero for sufficiently large number of collocation points.