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Bernstein collocation method for solving MHD Jeffery-Hamel blood flow problem with error estimations. (English) Zbl 07610791

MSC:

65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76Wxx Magnetohydrodynamics and electrohydrodynamics
65Dxx Numerical approximation and computational geometry (primarily algorithms)
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[1] Jeffery, G. B., L The two-dimensional steady motion of a viscous fluid, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 29, 172, 455-465 (1915) · JFM 45.1088.01 · doi:10.1080/14786440408635327
[2] Marinca, V.; Herişanu, N., An optimal homotopy asymptotic approach applied to nonlinear MHD Jeffery-Hamel flow, Mathematical Problems in Engineering, 2011 (2011) · Zbl 1235.76110 · doi:10.1155/2011/169056
[3] Khan, U.; Sikandar, W.; Ahmed, N.; Din, S. T. M.; Ahmed, N., Effects of velocity slip on MHD flow of a non-Newtonian fluid in converging and diverging channels, International Journal of Algorithms, Computing and Mathematics, 2, 4, 469-483 (2016) · Zbl 1421.76269 · doi:10.1007/s40819-015-0071-5
[4] Jamil, D. F.; Saleem, S.; Roslan, R.; Mubaddel, F. S. A.; Gorji, M. R.; Issakhov, A.; Din, S. U., Analysis of non-Newtonian magnetic Casson blood flow in an inclined stenosed artery using Caputo-Fabrizio fractional derivatives, Computer Methods and Programs in Biomedicine, 203 (2021) · doi:10.1016/j.cmpb.2021.106044
[5] Nazeer, M.; Saleem, S.; Hussain, F.; Iftikhar, S.; Qahtani, A. A., Mathematical modeling of bio-magnetic fluid bounded by ciliated walls of wavy channel incorporated with viscous dissipation: discarding mucus from lungs and blood streams, International Communications in Heat and Mass Transfer, 124 (2021) · doi:10.1016/j.icheatmasstransfer.2021.105274
[6] Qasim, M.; Afridi, M. I.; Wakif, A.; Saleem, S., Influence of variable transport properties on nonlinear radioactive Jeffrey fluid flow over a disk: utilization of generalized differential quadrature method, Arabian Journal for Science and Engineering, 44, 6 (2019)
[7] Hamrelaine, S.; Oudina, F. M.; Rafik, M., Analysis of MHD Jeffery-Hamel flow with suction/injection by homotopy analysis method, J. Adv. Res. Fluid Mech. Therm. Sci., 58, 173-186 (2019)
[8] Ara, A.; Khan, N. A.; Naz, F.; Raja, M. A. Z.; Rubbab, Q., Numerical simulation for Jeffery-Hamel flow and heat transfer of micropolar fluid based on differential evolution algorithm, AIP Advances, 8, 1 (2018) · doi:10.1063/1.5011727
[9] Mahmood, A.; Basir, M. F. M.; Ali, U.; Kasihmuddin, M. S. M.; Mansor, M. A., Numerical solutions of heat transfer for magnetohydrodynamic Jeffery-Hamel flow using spectral homotopy analysis method, Processes, 7, 9 (2019) · doi:10.3390/pr7090626
[10] Adel, W.; Biçer, K. E.; Sezer, M., A novel numerical approach for simulating the nonlinear MHD Jeffery-Hamel flow problem, International Journal of Algorithms, Computing and Mathematics, 7, 3, 74-15 (2021) · Zbl 1499.76137 · doi:10.1007/s40819-021-01016-3
[11] Coluccio, L.; Eisinberg, A.; Fedele, G., Gauss-Lobatto to Bernstein polynomials transformation, Journal of Computational and Applied Mathematics, 222, 2, 690-700 (2008) · Zbl 1157.65013 · doi:10.1016/j.cam.2007.12.007
[12] Lorentz, G. G., Bernstein Polynomials (2013), Providence, RI, USA: American Mathematical Soc, Providence, RI, USA
[13] Jafarian, A.; Nia, S. A. M.; Golmankhaneh, A. K.; Baleanu, D., Numerical solution of linear integral equations system using the Bernstein collocation method, Advances in Difference Equations, 2013, 1 (2013) · Zbl 1444.65077 · doi:10.1186/1687-1847-2013-123
[14] Hammad, D. A., Application of Bernstein collocation method for solving the generalized regularized long wave equations, Ain Shams Engineering Journal, 12, 4, 4081-4089 (2021) · doi:10.1016/j.asej.2021.04.005
[15] Ali, I., Bernstein collocation method for neutral type functional differential equation, Mathematical Biosciences and Engineering, 18, 3, 2764-2774 (2021) · Zbl 1523.65064 · doi:10.3934/mbe.2021140
[16] Mohammad, S. H.; Rawi, E. S. A., Solving fractional coupled EW and coupled MEW equations using Bernstein collocation method, Journal of Physics: Conference Series, 1804 (2021) · doi:10.1088/1742-6596/1804/1/012021
[17] Bataineh, A. S.; Isik, O. R.; Oqielat, M. A. N.; Hashim, I., An enhanced adaptive Bernstein collocation method for solving systems of ODEs, Mathematics, 9, 4, 425 (2021) · doi:10.3390/math9040425
[18] Shahni, J.; Singh, R., Numerical solution of system of Emden-Fowler type equations by Bernstein collocation method, Journal of Mathematical Chemistry, 59, 4, 1117-1138 (2021) · Zbl 1471.65090 · doi:10.1007/s10910-021-01235-5
[19] Shahni, J.; Singh, R., An efficient numerical technique for Lane-Emden-Fowler boundary value problems: Bernstein collocation method, The European Physical Journal Plus, 135, 6 (2020) · doi:10.1140/epjp/s13360-020-00489-3
[20] Shahni, J.; Singh, R., Numerical results of Emden-Fowler boundary value problems with derivative dependence using the Bernstein collocation method, Engineering with Computers, 38, 371-380 (2022) · doi:10.1007/s00366-020-01155-z
[21] Ahmad, I.; Ilyas, H., Homotopy perturbation method for the nonlinear MHD Jeffery-Hamel blood flows problem, Applied Numerical Mathematics, 141, 124-132 (2019) · Zbl 1418.92031 · doi:10.1016/j.apnum.2018.07.005
[22] Schlichting, H.; Gersten, K., Boundary-layer Theory (2000), New York, NY, USA: McGraw-Hill, New York, NY, USA · Zbl 0940.76003
[23] Bhatti, M. I.; Bracken, P., Solutions of differential equations in a Bernstein polynomial basis, Journal of Computational and Applied Mathematics, 205, 1, 272-280 (2007) · Zbl 1118.65087 · doi:10.1016/j.cam.2006.05.002
[24] Dascioglu, A.; Isler, N., Bernstein collocation method for solving nonlinear differential equations, Mathematical and Computational Applications, 18, 3, 293-300 (2013) · Zbl 1396.65123 · doi:10.3390/mca18030293
[25] Bataineh, A. S.; Isik, O. R.; Hashim, I., Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall, Alexandria Engineering Journal, 55, 3, 2149-2156 (2016) · doi:10.1016/j.aej.2016.06.022
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