Approximate collocation method for an integral equation with a logarithmic kernel (Q1375665)

The author considers the integral operator \(L\), \[ L\varphi= {1\over\pi} \int^1_{-1} \ln|x-t|{\varphi(t)\over\sqrt{1- t^2}} dt,\quad |x|\leq 1 \] and obtains an approximate solution of the integral equation \[ L\varphi= f \] using a quadrature method. The convergence of the proposed method is proved and an error bound is derived.