High-order compact scheme for the two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

Advances in Difference Equations

article

Khan, Muhammad Asim¹  Ali, Norhashidah Hj. Mohd¹ 

[1] School of Mathematical Sciences, Universiti Sains Malaysia

关键词: Two-dimensional fractional Rayleigh–Stokes;    Crank Nicolson;    High-order compact scheme;    Stability and convergence;   

DOI  :  10.1186/s13662-020-02689-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this article, an unconditionally stable compact high-order iterative finite difference scheme is developed on solving the two-dimensional fractional Rayleigh–Stokes equation. A relationship between the Riemann–Liouville (R–L) and Grunwald–Letnikov (G–L) fractional derivatives is used for the time-fractional derivative, and a fourth-order compact Crank–Nicolson approximation is applied for the space derivative to produce a high-order compact scheme. The stability and convergence for the proposed method will be proven; the proposed method will be shown to have the order of convergence $O(\tau + h^{4})$. Finally, numerical examples are provided to show the high accuracy solutions of the proposed scheme.

【 授权许可】

CC BY