A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid
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 resulti...
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SpringerOpen
2020-10-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03061-6 |
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doaj-58fa5f4dd3474b45b823fae07e1f641d2020-11-25T03:57:08ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020112210.1186/s13662-020-03061-6A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluidMuhammad Asim Khan0Norhashidah Hj. Mohd Ali1Nur Nadiah Abd Hamid2School of Mathematical Sciences, Universiti Sains MalaysiaSchool of Mathematical Sciences, Universiti Sains MalaysiaSchool of Mathematical Sciences, Universiti Sains MalaysiaAbstract 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.http://link.springer.com/article/10.1186/s13662-020-03061-6Two-dimensional fractional Rayleigh–Stokes problemFinite difference methodExplicit group methodCrank–Nicolson high-orderStability and convergence |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Muhammad Asim Khan Norhashidah Hj. Mohd Ali Nur Nadiah Abd Hamid |
| spellingShingle |
Muhammad Asim Khan Norhashidah Hj. Mohd Ali Nur Nadiah Abd Hamid A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid Advances in Difference Equations Two-dimensional fractional Rayleigh–Stokes problem Finite difference method Explicit group method Crank–Nicolson high-order Stability and convergence |
| author_facet |
Muhammad Asim Khan Norhashidah Hj. Mohd Ali Nur Nadiah Abd Hamid |
| author_sort |
Muhammad Asim Khan |
| title |
A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid |
| title_short |
A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid |
| title_full |
A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid |
| title_fullStr |
A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid |
| title_full_unstemmed |
A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid |
| title_sort |
new fourth-order explicit group method in the solution of two-dimensional fractional rayleigh–stokes problem for a heated generalized second-grade fluid |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2020-10-01 |
| description |
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. |
| topic |
Two-dimensional fractional Rayleigh–Stokes problem Finite difference method Explicit group method Crank–Nicolson high-order Stability and convergence |
| url |
http://link.springer.com/article/10.1186/s13662-020-03061-6 |
| work_keys_str_mv |
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