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Numerical quasilinearization scheme for the integral equation form of the Blasius equation | ||
| Computational Methods for Differential Equations | ||
| مقاله 3، دوره 6، شماره 2، تیر 2018، صفحه 141-156 اصل مقاله (216.05 K) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Esmaeil Najafi* | ||
| Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran | ||
| چکیده | ||
| The method of quasilinearization is an effective tool to solve nonlinear equations when some conditions on the nonlinear term of the problem are satisfied. When the conditions hold, applying this technique gives two sequences of coupled linear equations and the solutions of these linear equations are quadratically convergent to the solution of the nonlinear problem. In this article, using some transformations, the well-known Blasius equation which is a nonlinear third order boundary value problem, is converted to a nonlinear Volterra integral equation satisfying the conditions of the quasilinearization scheme. By applying the quasilinearization, the solutions of the obtained linear integral equations are approximated by the collocation method. Employing the inverse of the transformation gives the approximation solution of the Blasius equation. Error analysis is performed and comparison of results with the other methods shows the priority of the proposed method. | ||
| کلیدواژهها | ||
| Quasilinearization technique؛ Volterra integral equations؛ Blasius equation؛ Collocation method | ||
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آمار تعداد مشاهده مقاله: 451 تعداد دریافت فایل اصل مقاله: 577 |
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