An alternating direction implicit legendre spectral method for simulating a 2D multi-term time-fractional Oldroyd-B fluid type diffusion equation. (1st May 2022)

• Record Type: Journal Article
• Authors: Liu, Yanqin; Yin, Xiuling; Liu, Fawang; Xin, Xiaoyi; Shen, Yanfeng; Feng, Libo
• Is Part Of: Computers & mathematics with applications. Volume 113(2022)
• Page Start: 160
• Page End: 173
• Publication Date: 2022-05-01
• Subjects: Multi-term time fractional equation -- Oldroyd-B fluid model -- ADILS method -- Stability and convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.03.020
• Languages: English
• ISSNs: 0898-1221

Abstract

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.