Reproducing kernel method for solving wiener-hopf equations of the second kind

This paper proposed a reproducing kernel method for solving Wiener-Hopf equations of the second kind. In order to eliminate the singularity of the equation, a transform is used. The advantage of this numerical method is the representation of exact solution in reproducing kernel Hilbert space and accuracy in numerical computation is higher. On the other hand, by improving the traditional reproducing kernel method and the definition of the operator of W Hilbert space, the solutions of Wiener Hopf equation of the second kind are obtained. The approximate solution converges uniformly and rapidly to the exact solution. Numerical examples indicate that this method is efficient for solving these equations. The validity of the method is illustrated with two examples.

Keywords:

Reproducing kernel method , Wiener-Hopf equation , Singular integral equation.