Analysis of collocation methods for nonlinear Volterra integral equations of the third kind (Q666607)

For a nonlinear Volterra integral equation of the third kind \[t^{\beta}u(t) = t^{\beta}f(t) + \int_{0}^{t}k(t,s)G(u(s))\,ds\] with $t\in I = [0,T]$, $\beta\in(0,1]$, $f\in C(I)$, $k\in C(D)$, where $D=\lbrace (t,s): 0\le s\le t\le T\rbrace$, $G\in C^{(1)}(\mathbb{R})$, the authors investigate the convergence of collocation methods in some class of piecewise polynomial spaces. The convergence order is investigated. The paper contains several results of numerical experiments.