A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

• Main Authors: Muhammad Asim Khan, Norhashidah Hj. Mohd Ali, Nur Nadiah Abd Hamid
• Format: Article
• Language: English
• Published: SpringerOpen 2020-10-01
• Series: Advances in Difference Equations
• Subjects: Two-dimensional fractional Rayleigh–Stokes problem; Finite difference method; Explicit group method; Crank–Nicolson high-order; Stability and convergence
• Online Access: http://link.springer.com/article/10.1186/s13662-020-03061-6
• ISSN: 1687-1847

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.