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Adiyaman, Meltem, Beler, Ayşe. (1402). Improved residual method for approximating Bratu problem. سامانه مدیریت نشریات علمی, 11(3), 535-547. doi: 10.22034/cmde.2022.52605.2208
Meltem Adiyaman; Ayşe Beler. "Improved residual method for approximating Bratu problem". سامانه مدیریت نشریات علمی, 11, 3, 1402, 535-547. doi: 10.22034/cmde.2022.52605.2208
Adiyaman, Meltem, Beler, Ayşe. (1402). 'Improved residual method for approximating Bratu problem', سامانه مدیریت نشریات علمی, 11(3), pp. 535-547. doi: 10.22034/cmde.2022.52605.2208
Adiyaman, Meltem, Beler, Ayşe. Improved residual method for approximating Bratu problem. سامانه مدیریت نشریات علمی, 1402; 11(3): 535-547. doi: 10.22034/cmde.2022.52605.2208

Improved residual method for approximating Bratu problem

Computational Methods for Differential Equations
مقاله 7، دوره 11، شماره 3، شهریور 2023، صفحه 535-547    اصل مقاله (242.75 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.52605.2208
نویسندگان
Meltem Adiyaman* 1؛ Ayşe Beler2
1Department of Mathematics, Faculty of Sciences, Dokuz Eyl¨ul University, Tınaztepe, Buca, 35160 Izmir, Turkey.
2The Graduate School of Natural and Applied Sciences, Dokuz Eyl¨ul University, Tınaztepe, Buca, 35160 Izmir, Turkey.
چکیده
In this study,  firstly, the residual method, which was developed for initial value problems, is improved to find unknown coefficients without requiring for any system solution. Later, the adaptation of improved residual method is given to find approximate solutions of boundary value problems. Finally, the method improved and adapted for boundary value problems is used to find both critical eigenvalue and eigenfunctions of the one-dimensional Bratu problem. The most significant advantage of the method is finding approximate solutions of nonlinear problems without any linearization or solving any system of equations. Error analysis of the adapted method is given and an upper bound on the approximation error is derived for the eigenfunctions. The numerical results obtained are compared with the theoretical findings. Comparisons and theoretical observations show that the improved and adapted method is very convenient and successful in solving boundary value problems and eigenvalue problems approximately with high accuracy.
کلیدواژه‌ها
Bratu Problem؛ Bezier curves؛ Residual method؛ Error analysis
مراجع
  • [1] M.  B.   Abd-el-Malek,   A.   Abdelrazek,   M.   Ghazy,   and   G.   Gamal,   A   modified   perturbation   solution   to one dimensional Bratu problem, Applied Mathematics and Computation, 354 (2019), 296–304.
  • [2] M. Adyaman and V. Oger, A residual method using B´ezier curves for singular nonlinear equations of Lane-Emden type, Kuwait Journal of Science, 44(4) (2017), 9–18.
  • [3] M. E. Adyaman and S. Somali, Taylors decomposition on two points for one-dimensional Bratu problem, Numerical Methods for Partial Differential Equations, 26(2) (2010), 412–425.
  • [4] A. N. Al-Janabi, F.J. Al Zahed, and A. H. Hussain, An  approximate solution of integral equation using Bezier control Points, International Journal of Nonlinear Analysis and Applications, 12(2) (2021), 793–798.
  • [5] R. Buckmire, Application of a Mickens finite difference scheme to the cylindrical Bratu-Gelfand problem, Numer- ical Methods for Partial Differential Equations, 20 (2004), 327–337.
  • [6] R. Buckmire, On Exact and Numerical Solutions of the One-Dimensional Planar Bratu Problem, Mathematics eJournal, (2003).
  • [7] S. Chandrasekhar, An introduction to the study of stellar structure, Dover Publications Inc., New York, 1957.
  • [8] D. A. Frank-Kamenetski, Difussion and heat exchange in chemical kinetics, Princeton University Press, Princeton NJ, 1995.
  • [9] N. Ghaderi and M. H. Farahi, The Numerical Solution of Nonlinear Optimal Control Problems by  Using  Opera-  tional Matrix of Bernstein Polynomials, Mathematical Analysis and Convex Optimization, 2(1) (2021), 11–27.
  • [10] F. Ghomanjani, A numerical method for solving Bratu’s Problem, Palestine Journal of Mathematics, 11(2) (2022), 372–377.
  • [11] F. Ghomanjani and M. H. Farahi, The Bezier Control Points Method for Solving Delay Differential Equation, Intelligent Control and Automation, 3 (2012), 188–196.
  • [12] J. Jacobsen and K. Schmitt, The Liouville-Bratu-Gelfand problem for radial operators, Journal of Differential Equations, 184 (2002), 283–298.
  • [13] N. Karamollahi, G. B. Loghmani, and M. Heydari, A computaional method to find dual solutions of the one- dimensional Bratu problem, Journal of Computational and Applied Mathematics, 388 (2021), 113309.
  • [14] E. Keshavarz, Y. Ordokhani and M. Razzaghi, The Taylor wavelets method for solving the initial  and  boundary  value problems of Bratu-type equations, Applied Numerical Mathematics, 128 (2018), 205–216.
  • [15] S. A. Odejide and Y. A. S. Aregbesola, A note on two dimensional Bratu problem, Kragujevac Journal of Math- ematics, 29 (2007), 49–56.
  • [16] V. Oger, Numerical Solutions of Differential Equations Using  Residual  Method,  2016,  Thesis  (Ph.D.),  Dokuz  Eylul University-Turkey.
  • [17] O. Ragb, L. F. Seddek and M.S.Matbuly, Iterative differential quadrature solutions for Bratu problem, Computers and Mathematics with Applications, 74(2) (2017), 249–257.
  • [18] H. Temimi and M. B. Romdhane, An iterative finite difference method for solving Bratu’s problem, Journal of Computational and Applied Mathematics, 292 (2016), 76–82.
  • [19] A. M. Wazwaz, The successive differentiation method for solving Bratu equation and Bratu-type equations, Ro- manian Journal of Physics, 61 (2016), 774–783.
  • [20] C. Yang and J. Hou, Chebyshev wavelets method for solving Bratu’s problem, Boundary Value Problems, 142 (2013).
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