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

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...

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Bibliographic Details
Published in:Advances in difference equations 2020-10, Vol.2020 (1), p.1-22, Article 598
Main Authors: Khan, Muhammad Asim, Ali, Norhashidah Hj. Mohd, Hamid, Nur Nadiah Abd
Format: Article
Language:English
Subjects:
Analysis
Computational fluid dynamics
Crank–Nicolson high-order
Difference and Functional Equations
Energy methods
Explicit group method
Finite difference method
Functional Analysis
Iterative methods
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Stability and convergence
Two-dimensional fractional Rayleigh–Stokes problem
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03061-6