Numerical solution of integral equations with finite part integrals (Q1283415)

The paper is devoted to approximate methods (Galerkin method and mechanical quadrature method) for the solution of integral equations of the form \[ {1\over\pi} \int^\pi_{-\pi} {\sqrt{1-\tau^2} x(\tau)\over(\tau-t)^2} d\tau +\int^\pi_{-\pi} \sqrt{1-\tau^2} h(t,\tau)x (\tau)d \tau=f(t). \] The convergence and exactness of these methods are investigated.