Research Article
Year 2020,
Volume: 33 Issue: 1, 168 - 186, 01.03.2020
Abstract
References
- [1] Duque-Daza, C., Lockerby, D. and Galeano, C., "Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes", Journal of the Brazilian Society of Mechanical Sciences and Engineering 33(4):381-392, (2011).[2] Bakodah, H. O., Ebaid, A. and Wazwaz, A. M., "Analytical and Numerical Treatment Of Falkner-Skan Equation Via A Transformation And Adomian’s Method", Romanian Reports in Physics, (2017)( In press).
- [3] Dehghan, M., Tatari, M. and Azizi, A., " The solution of the Falkner-Skan equation arising in the modelling of boundary-layer problems via variational iteration method", International Journal of Numerical Methods for Heat . Fluid Flow. 21(2): 136-149, (2011).[4] Eerdun,B., Eerdun ,Q., Huhe, B., Temuer, C. and Wang , J. Y., "Variational iteration method with He's polynomials for MHD Falkner-Skan flow over permeable wall based on Lie symmetry method", International Journal of Numerical Methods for Heat . Fluid Flow. 24(6): 1348-1362, (2014).[5] Madaki,A. G., Ali, M. M., and Roslan, R.," Solution of the Falkner–Skan wedge flow by a revised optimal homotopy asymptotic method", Springer Plus. 5(1): 513, (2016).[6] Temimi, H. and Ben-Romdhane ,M., "Numerical solution of falkner-skan equation by iterative transformation method", Mathematical Modelling and Analysis. 23(1): 139-151, (2018).[7] Shafieenejad, N. I., Hashemi, S. F., Fata, A., "Approximate explicit solution of falkner-skan equation by homotopy perturbation method", Research Journal of Applied Sciences, Engineering and Technology, 4(17): 2893-2897, (2012).
- [8] Yao, B., "Approximate analytical solution to the Falkner–Skan wedge flow with the permeable wall of uniform suction", Communications in Nonlinear Science and Numerical Simulation,14(8): 3320-3326, (2009).
- [9] Summiya, P., "Numerical solution of the Falkner Skan Equation by using shooting techniques", IOSR Journal of Mathematics, 10( 6): 78-83, ( 2014).
- [10] Kajani, M.T., Maleki, M. and Allame, M., "A numerical solution of Falkner-Skan equation via a shifted Chebyshev collocation method", AIP Conference Proceedings, 1629(1): 381-386, (2014).
- [11] AKYÜZ-DAŞCIOĞLU, A., ACAR, N. I.. Bernstein Collocation Method for Solving Linear Differential Equations. Gazi University Journal of Science, 26(4): 527-534, (2013). [12] Ali, A., Min Ullah, Z., Uddin M.," On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels", Gazi University Journal of Science 31(3): 879-888, (2018).
- [13] BAYKUŞ SAVAŞANERİL, N., HACIOĞLU, Z., "Bernstein Series Approximation for Dirichlet Problem", Gazi University Journal of Science, 31(2): 544-553, (2018).[14] Daftardar-Gejji ,V., Jafari ,H., "An iterative method for solving nonlinear functional equations", Journal of Mathematical Analysis and Applications, 316(2): 753-763, (2006).
- [15] Bhalekar, S., Daftardar-Gejji ,V., "New iterative method: Application to partial differential equations",Applied Mathematics and Computation, 203(2): 778-783, (2008) [16] Daftardar-Gejji ,V., Bhalekar ,S., "Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method", Computers and Mathematics with Applications, 59(5): 1801-1809, (2010). [17] AL-Jawary ,M. A., Abd-AL-Razaq ,S. G.," Analytic and numerical solution for Duffing equations", International Journal of Basic and Applied Sciences, 5(2): 115- 119, (2016). [18] ] Yaseen, M., Samraiz ,M.and Naheed,S., "The DJ method for exact solutions of Laplace equation",Results in Physics, 3, 38-40, (2013).[19] Ehsani, F., Hadi, A., Ehsani, F. and Mahdavi, R., "An iterative method for solving partial differential equations and solution of Korteweg-de Vries equations for showing the capability of the iterative method", World Applied Programming,3(8) : 320–327, (2013).[20] Temimi, H., Ansari, A. R., "A computational iterative method for solving nonlinear ordinary differential equations",LMS Journal of Computation and mathematics", 18 (1): 730–753, (2015).[21] AL-Jawary, M. A., AL-Qaissy, H. R., "A reliable iterative method for solving Volterra integro-differential equations and some applications for the Lane-Emden equations of the first kind", Monthly Notices of the Royal Astronomical Society, 448(4): 3093-3104, (2015).[22] Temimi, H., Ansari, A. R., "A new iterative technique for solving nonlinear second order multi-point boundary value problems", Applied Mathematics and Computation, 218(4): 1457-1466, (2011).[23] ] AL-Jawary, M. A., Al-Razaq, S. G., "A semi analytical iterative technique for solving duffing equations", International Journal of pure and applied Mathematics, 108(4): 871-885, (2016).[24] AL-Jawary, M. A., Raham, R. K., "A semi-analytical iterative technique for solving chemistry problems", Journal of King Saud University,. 29 (3): 320-332, (2017). [25] AL-Jawary ,M. A., Hatif, S., "A semi-analytical iterative method for solving differential algebraic equations", Ain Shams Engineering Journal,(2017), (In Press).[26] AL-Jawary, M. A., "A semi-analytical iterative method for solving nonlinear thin film flow problems", Chaos. Solitons and Fractals, 99:52–56,(2017. [27] AL-Jawary, M. A., Radhi, G. H., and Ravnik, J., "A semi-analytical method for solving Fokker-Planck’s equations", Journal of the Association of Arab Universities for Basic and Applied Sciences, 24(1): 254-262, (2017).[28] Daftardar-Gejji ,V., Bhalekar, S., "Solving nonlinear functional equation using Banach contraction principle", Far East Journal of Applied Mathematics, 34(3): 303-314, (2009).[29] Latif, A., Banach contraction principle and its generalizations. Topics in Fixed Point Theory. Springer International Publishing, 33-64, (2014).
- [30] Ebaid, A., Aljoufi, M. D., Wazwaz, A. M., "An advanced study on the solution of nanofluid flow problems via Adomian’s method",Applied Mathematics Letters ,46: 117-122, (2015).[31] Bougoffa, L., Alqahtani, R. T., "Further Solutions Of The Falkner-Skan Equation",Romanian Journal Of Physics, 63,102, (2018).[32] Alpaslan, P. H., Oturanc ,G., "A Semi Analytical Analysis of a Free Convection Boundary Layer Flow Over a Vertical Plate". arXiv.org.1212.1706, (2012) . [33] Bhalekar, S., Patade, J. ," An Analytical Solution of Fisher’s Equation Us Decomposition Method",American Journal of Computational and Applied Mathematics, 6(3): 123-127, (2016). [34] Wazwaz, A. M., "A first course in integral equations. World Scientific Publishing Company, (2015).[35] Jiao, Y. C., Dang, C. and Yamamoto, Y., "An extension of the decomposition method for solving nonlinear equations and its convergence", Computers . Mathematics with Applications 55(4):760-775, (2008). [36] Odibat, Z. M., "A study on the convergence of variational iteration method", Mathematical and Computer Modelling, 51(9-10): 1181-1192, (2010).
Year 2020,
Volume: 33 Issue: 1, 168 - 186, 01.03.2020
Abstract
In this work, we suggest reliable iterative methods to solve the Falkner-Skan problem to obtain new approximate solutions. The suggested methods. are Tamimi-Ansari method.(TAM), Daftardair-Jafari. method.(DJM) and Banach countraction method.(BCM). We compare the obtained numerical results with other numerical methods like the Runge-Kutta (RK4) and Euler methods. The fixed point theorm is presented to test the convergence of the suggested methods. Moreover, the results of the remaining maximum error values showing that the suggested methods are reliable and effective. The Software used in our calculations for this work is Mathematica® 10.
References
- [1] Duque-Daza, C., Lockerby, D. and Galeano, C., "Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes", Journal of the Brazilian Society of Mechanical Sciences and Engineering 33(4):381-392, (2011).[2] Bakodah, H. O., Ebaid, A. and Wazwaz, A. M., "Analytical and Numerical Treatment Of Falkner-Skan Equation Via A Transformation And Adomian’s Method", Romanian Reports in Physics, (2017)( In press).
- [3] Dehghan, M., Tatari, M. and Azizi, A., " The solution of the Falkner-Skan equation arising in the modelling of boundary-layer problems via variational iteration method", International Journal of Numerical Methods for Heat . Fluid Flow. 21(2): 136-149, (2011).[4] Eerdun,B., Eerdun ,Q., Huhe, B., Temuer, C. and Wang , J. Y., "Variational iteration method with He's polynomials for MHD Falkner-Skan flow over permeable wall based on Lie symmetry method", International Journal of Numerical Methods for Heat . Fluid Flow. 24(6): 1348-1362, (2014).[5] Madaki,A. G., Ali, M. M., and Roslan, R.," Solution of the Falkner–Skan wedge flow by a revised optimal homotopy asymptotic method", Springer Plus. 5(1): 513, (2016).[6] Temimi, H. and Ben-Romdhane ,M., "Numerical solution of falkner-skan equation by iterative transformation method", Mathematical Modelling and Analysis. 23(1): 139-151, (2018).[7] Shafieenejad, N. I., Hashemi, S. F., Fata, A., "Approximate explicit solution of falkner-skan equation by homotopy perturbation method", Research Journal of Applied Sciences, Engineering and Technology, 4(17): 2893-2897, (2012).
- [8] Yao, B., "Approximate analytical solution to the Falkner–Skan wedge flow with the permeable wall of uniform suction", Communications in Nonlinear Science and Numerical Simulation,14(8): 3320-3326, (2009).
- [9] Summiya, P., "Numerical solution of the Falkner Skan Equation by using shooting techniques", IOSR Journal of Mathematics, 10( 6): 78-83, ( 2014).
- [10] Kajani, M.T., Maleki, M. and Allame, M., "A numerical solution of Falkner-Skan equation via a shifted Chebyshev collocation method", AIP Conference Proceedings, 1629(1): 381-386, (2014).
- [11] AKYÜZ-DAŞCIOĞLU, A., ACAR, N. I.. Bernstein Collocation Method for Solving Linear Differential Equations. Gazi University Journal of Science, 26(4): 527-534, (2013). [12] Ali, A., Min Ullah, Z., Uddin M.," On the Approximation of Highly Oscillatory Integral Equations Via Radial Kernels", Gazi University Journal of Science 31(3): 879-888, (2018).
- [13] BAYKUŞ SAVAŞANERİL, N., HACIOĞLU, Z., "Bernstein Series Approximation for Dirichlet Problem", Gazi University Journal of Science, 31(2): 544-553, (2018).[14] Daftardar-Gejji ,V., Jafari ,H., "An iterative method for solving nonlinear functional equations", Journal of Mathematical Analysis and Applications, 316(2): 753-763, (2006).
- [15] Bhalekar, S., Daftardar-Gejji ,V., "New iterative method: Application to partial differential equations",Applied Mathematics and Computation, 203(2): 778-783, (2008) [16] Daftardar-Gejji ,V., Bhalekar ,S., "Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method", Computers and Mathematics with Applications, 59(5): 1801-1809, (2010). [17] AL-Jawary ,M. A., Abd-AL-Razaq ,S. G.," Analytic and numerical solution for Duffing equations", International Journal of Basic and Applied Sciences, 5(2): 115- 119, (2016). [18] ] Yaseen, M., Samraiz ,M.and Naheed,S., "The DJ method for exact solutions of Laplace equation",Results in Physics, 3, 38-40, (2013).[19] Ehsani, F., Hadi, A., Ehsani, F. and Mahdavi, R., "An iterative method for solving partial differential equations and solution of Korteweg-de Vries equations for showing the capability of the iterative method", World Applied Programming,3(8) : 320–327, (2013).[20] Temimi, H., Ansari, A. R., "A computational iterative method for solving nonlinear ordinary differential equations",LMS Journal of Computation and mathematics", 18 (1): 730–753, (2015).[21] AL-Jawary, M. A., AL-Qaissy, H. R., "A reliable iterative method for solving Volterra integro-differential equations and some applications for the Lane-Emden equations of the first kind", Monthly Notices of the Royal Astronomical Society, 448(4): 3093-3104, (2015).[22] Temimi, H., Ansari, A. R., "A new iterative technique for solving nonlinear second order multi-point boundary value problems", Applied Mathematics and Computation, 218(4): 1457-1466, (2011).[23] ] AL-Jawary, M. A., Al-Razaq, S. G., "A semi analytical iterative technique for solving duffing equations", International Journal of pure and applied Mathematics, 108(4): 871-885, (2016).[24] AL-Jawary, M. A., Raham, R. K., "A semi-analytical iterative technique for solving chemistry problems", Journal of King Saud University,. 29 (3): 320-332, (2017). [25] AL-Jawary ,M. A., Hatif, S., "A semi-analytical iterative method for solving differential algebraic equations", Ain Shams Engineering Journal,(2017), (In Press).[26] AL-Jawary, M. A., "A semi-analytical iterative method for solving nonlinear thin film flow problems", Chaos. Solitons and Fractals, 99:52–56,(2017. [27] AL-Jawary, M. A., Radhi, G. H., and Ravnik, J., "A semi-analytical method for solving Fokker-Planck’s equations", Journal of the Association of Arab Universities for Basic and Applied Sciences, 24(1): 254-262, (2017).[28] Daftardar-Gejji ,V., Bhalekar, S., "Solving nonlinear functional equation using Banach contraction principle", Far East Journal of Applied Mathematics, 34(3): 303-314, (2009).[29] Latif, A., Banach contraction principle and its generalizations. Topics in Fixed Point Theory. Springer International Publishing, 33-64, (2014).
- [30] Ebaid, A., Aljoufi, M. D., Wazwaz, A. M., "An advanced study on the solution of nanofluid flow problems via Adomian’s method",Applied Mathematics Letters ,46: 117-122, (2015).[31] Bougoffa, L., Alqahtani, R. T., "Further Solutions Of The Falkner-Skan Equation",Romanian Journal Of Physics, 63,102, (2018).[32] Alpaslan, P. H., Oturanc ,G., "A Semi Analytical Analysis of a Free Convection Boundary Layer Flow Over a Vertical Plate". arXiv.org.1212.1706, (2012) . [33] Bhalekar, S., Patade, J. ," An Analytical Solution of Fisher’s Equation Us Decomposition Method",American Journal of Computational and Applied Mathematics, 6(3): 123-127, (2016). [34] Wazwaz, A. M., "A first course in integral equations. World Scientific Publishing Company, (2015).[35] Jiao, Y. C., Dang, C. and Yamamoto, Y., "An extension of the decomposition method for solving nonlinear equations and its convergence", Computers . Mathematics with Applications 55(4):760-775, (2008). [36] Odibat, Z. M., "A study on the convergence of variational iteration method", Mathematical and Computer Modelling, 51(9-10): 1181-1192, (2010).
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | March 1, 2020 |
| Published in Issue | Year 2020 Volume: 33 Issue: 1 |