A Note on Solving Prandtl's Integro-Differential Equation

International Journal of Mathematical Modelling & Computations

مقاله 2، دوره 7، 4 (FALL) - شماره پیاپی 28، بهمن 2017، صفحه 255-263   

نوع مقاله: Full Length Article

نویسندگان

Atta Dezhbord^* ؛ Taher Lotfi

Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65138, Iran

چکیده

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its advantages are that the representation of the exact solution is obtained in a reproducing kernel Hilbert space and accuracy in numerical computation is higher. On the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives. The final numerical experiments illustrate the method is efficient.

کلیدواژه‌ها

Reproducing Kernel Space؛ Singular integro-differential equation of Prandtl's type؛ Hypersingular integral equation؛ Error estimation