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On solving Bratu’s type equation by perturbation method | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 226، دوره 13، شماره 1، خرداد 2022، صفحه 2755-2763 اصل مقاله (394.54 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6000 | ||
| نویسندگان | ||
| Safaa Ali Salem؛ Thair Younis Thanoon* | ||
| College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq | ||
| تاریخ دریافت: 21 شهریور 1400، تاریخ بازنگری: 26 مهر 1400، تاریخ پذیرش: 03 آذر 1400 | ||
| چکیده | ||
| In this paper, the perturbation method is employed to obtain an approximate solution of some examples of the Bratu equation by choosing the different values of $ \varepsilon $ and comparison with the exact solutions. It can be seen that the perturbation method is an alternative technique to be considered in solving many practical problems involving differential equations. | ||
| کلیدواژهها | ||
| Non-linear differential equation؛ Perturbation method, Bratu's type equation, Approximate solution | ||
| مراجع | ||
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[1] Y. Aregbesola, Numerical solution of Bratu problem using the method of weighted residual, Elect. J. South African Math. Soc. 3(1) (2003) 1–7. [2] R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalyst, Oxford University Press, Clarendon, 1, 1975. [3] U.M. Ascher, R.M.M. Mattheij and R.D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, 1st Edn., SIAM, Philadelphia, 1994. [4] J. Bebernes and D. Eberly, Mathematical Problems From Combustion Theory, Springer Science & Business Media, Springer-Verlag, 1989. [5] S. Chandrasekhar, Introduction to the Study of Stellar Structure, Dover, New York, 1967. [6] Y. Changqing and H. Jianhua, Chebyshev wavelets method for solving Bratu’s problem, Bound. Value Prob. 2013(1) (2013) 1–9. [7] T.L. Chow, Classical Mechanics, John Wiley and Sons Inc., USA, 1995. [8] N. Cohen and J. Benavides, Exact solutions of bratu and liouville equations, CNMAC 2010 (2010) 750–756. [9] A. Ezekiel, New Improved Variational Homotopy Perturbation Method for Bratu-Type Problems, Amer. J. Comput. Math. 3(2) (2013) 110–113. [10] H.B. Fenta and G.A. Derese, Numerical solution of second order initial value problems of Bratu-type equations using sixth-order Runge-Kutta seven stages method, Int. J. Comput. Sci. Appl. Math. 5(1) (2019). [11] H.N. Hassan and M. S. Semary, Analytic approximate solution for the Bratu’s problem by optimal homotopy analysis method, Commun. Numerical Anal. 2013 (2013), 1-14. [12] M.H. Holmes, Introduction to Perturbation Methods, Springer-Verlag, New York, 1995. [13] A. Mohsen, A simple solution of the Bratu problem, J. Comput. Math. Appl. 67 (2014) 26–33. [14] J. Rashidinia and N. Taher, Application of the Sinc approximation to the solution of Bratu’s problem, Int. J. Math. Model. Comput. 2(3) (2012) 239–246. [15] M. Saravi, M. Hermann and D. Kaiser, Solution of Bratu’s Equation by He’s variational Iteration Method, Amer. J. Comput. Appl. Math. 3(1) (2013) 46–48. [16] A.M. Wazwaz, Adomians decomposition method for a reliable treatment of the Bratu-type equations, Appl. Math. Comput. 166 (2005) 652–663. [17] A.M. Wazwaz, The successive differentiation method for solving Bratu equation and Bratu-type equations, Rom. J. Phys. 61 (2016) 774–783. [18] M. Zarebnia and M. Hoshyar, Solution of Bratu-type equation via spline method, Acta Universities Apulensis 37 (2014) 61–72. | ||
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