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Application of cubic B-splines collocation method for solving nonlinear inverse diffusion problem | ||
| Computational Methods for Differential Equations | ||
| مقاله 8، دوره 7، شماره 3، مهر 2019، صفحه 434-453 اصل مقاله (560.34 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
Hamed Zeidabadi1؛ Reza Pourgholi  2؛ Seyed Hashem Tabasi2
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| 1Faculty of Engineering, Sabzevar University of New Technology, Sabzevar, Iran | ||
| 2School of Mathematics and Computer Science, Damghan University, P. O. Box 36715-364, Damghan, Iran | ||
| چکیده | ||
| In this paper, we developed a collocation method based on cubic B-spline for solving nonlinear inverse parabolic partial differential equations as the following form \begin{align*} u_{t} &= [f(u)\,u_{x}]_{x} + \varphi(x,t,u,u_{x}),\,\quad\quad 0 < x < 1,\,\,\, 0 \leq t \leq T, \end{align*} where $f(u)$ and $\varphi$ are smooth functions defined on $\mathbb{R}$. First, we obtained a time discrete scheme by approximating the first-order time derivative via forward finite difference formula, then we used cubic B-spline collocation method to approximate the spatial derivatives and Tikhonov regularization method for solving produced ill-posed system. It is proved that the proposed method has the order of convergence $O(k+h^2)$. The accuracy of the proposed method is demonstrated by applying it on three test problems. Figures and comparisons have been presented for clarity. The aim of this paper is to show that the collocation method based on cubic B-spline is also suitable for the treatment of the nonlinear inverse parabolic partial differential equations. | ||
| کلیدواژهها | ||
| Cubic B-spline؛ Collocation method؛ Inverse problems؛ Convergence analysis؛ Stability of solution؛ Tikhonov regularization method؛ Ill-posed problems؛ Noisy data | ||
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آمار تعداد مشاهده مقاله: 503 تعداد دریافت فایل اصل مقاله: 264 |
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