An alternating direction implicit legendre spectral method for simulating a 2D multi-term time-fractional Oldroyd-B fluid type diffusion equation

Abstract

In this paper, an alternating direction implicit legendre spectral (ADILS) method is developed for the two-dimensional (2D) multi-term time fractional Oldroyd-B fluid type diffusion equation. This method is provided based on legendre spectral approximation in space and a new difference discretization in time, and it can convert 2D computation to two 1D computations. Meanwhile, a very important lemma is proposed to prove the unconditional stability and convergence of this ADILS scheme. Especially, the corrected scheme is utilized to increase the convergence accuracy for the non-smooth solution. With three numerical experiments, the validity of the method is confirmed. The present method also can be extended to solve the generalized non-Newtonian fluid type equations, multi-term time fractional mixed diffusion and diffusion-wave equations.