A Note on Solving Prandtl's Integro-Differential Equation
Subject Areas : International Journal of Mathematical Modelling & Computations
Atta
Dezhbord
1
(Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65138, Iran)
Taher
Lotfi
2
(Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65138, Iran)
Keywords: Error estimation, Reproducing Kernel Space, Hypersingular integral equation, Singular integro-differential equation of Prandtl's type,
Abstract :
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.