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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
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