Fast iterative methods for solving of nonlinear weakly singular integral equations on smooth or nonsmooth boundary

When the collocation method is only used to solve the boundary integral equation (BNIE) on smooth or nonsmooth boundary, the singularities of the solution degrade the rates of convergence. We suggest variants of methods for finding numerical solutions. So, we have compared these methods with respect to CPU time and number of iterations. On the other hand, the existence and uniqueness of the solution for some kernel is proved. Numerical experiments show the efficiency of the proposed methods.