Discrete numerical solvability of Hammerstein integral equations of mixed type (Q920619)

The authors establish the convergence of some numerical methods for the solution of the integral equation \((1)\quad x(s)+\sum^{m}_{i=1}\int^{b}_{a}k_ i(s,t)f_ i(t,x(t))dt=y(s),\quad s\in [a,b].\) The methods are obtained representing (1) as an equivalent system of integral equations with respect to \(z_ i(s)=f_ i(s,x(s))\), \(i=1,...,m\), approximating \(z_ i\) by means of piecewise polynomial functions and collocation.