The approximate solution of nonlinear singular integro-differential equations (Q1182449)

The authors derive sufficient conditions for the convergence of the Newton-Kantorovich method (in a generalized Hölder space) for the nonlinear singular integro-differential equation with Hilbert kernel, \(u- A(u)=0\), where \(A(u):=(2\pi i)^{-1}\int^{2\pi}_ 0\Psi(\sigma,u(\sigma),u'(\sigma))\cot((\sigma-s)/2)d\sigma\). They also discuss the rate of convergence of the method.