A Note on Solving Prandtl's Integro-Dierential Equation

A simple method for solving Prandtl's integro-dierential 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 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 nal numerical experiments illustrate the method is ecient.