A Lie group integrator to solve the hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet

Mir Sajjad Hashemi; Hadi Rezazadeh; Hassan Almusawa; Hijaz Ahmad; Mir Sajjad Hashemi; Hadi Rezazadeh; Hassan Almusawa; Hijaz Ahmad

doi:10.3934/math.2021775

AIMS Mathematics

2021, Volume 6, Issue 12: 13392-13406. doi: 10.3934/math.2021775

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A Lie group integrator to solve the hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet

1.
Department of Mathematics, Basic Science Faculty, University of Bonab, P.O. Box 55513-95133, Bonab, Iran
2.
Faculty of Engineering Technology, Amol University of Special Modern Technological, Amol, Iran
3.
Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia
4.
Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
5.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

Received: 19 January 2021 Accepted: 06 September 2021 Published: 17 September 2021
MSC : 34Bxx, 34A26, 65Lxx

In the present paper, a Lie-group integrator, based on $ GL(4, \mathbb{R}) $ has been newly constructed to consider the flow characteristics in an electrically conducting second grade fluid over a stretching sheet. Present method which have a very fast convergence, permits us to explore some missing initial values at the left-end. Accurate initial values can be achieved when the determined target equation is valid, and then we can apply the group preserving scheme (GPS) as a geometric approach to obtain a rather accurate numerical solution. Finally, effects of magnetic parameter, viscoelastic parameter, stagnation point flow and stretching of the sheet parameters are illustrated.
- $ GL(4, \mathbb{R}) $ Lie group method,
- group preserving scheme,
- second grade fluid,
- stagnation point flow
Citation: Mir Sajjad Hashemi, Hadi Rezazadeh, Hassan Almusawa, Hijaz Ahmad. A Lie group integrator to solve the hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet[J]. AIMS Mathematics, 2021, 6(12): 13392-13406. doi: 10.3934/math.2021775

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Abstract

In the present paper, a Lie-group integrator, based on $ GL(4, \mathbb{R}) $ has been newly constructed to consider the flow characteristics in an electrically conducting second grade fluid over a stretching sheet. Present method which have a very fast convergence, permits us to explore some missing initial values at the left-end. Accurate initial values can be achieved when the determined target equation is valid, and then we can apply the group preserving scheme (GPS) as a geometric approach to obtain a rather accurate numerical solution. Finally, effects of magnetic parameter, viscoelastic parameter, stagnation point flow and stretching of the sheet parameters are illustrated.

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