A family of methods for Abel integral equations of the second kind (Q758174)

The following second kind nonlinear Abel integral equation \(y(t)=g(t)+\int^{t}_{0}(t-s)^{-\alpha}k(t,s,y(s))ds,\quad t\in [0,T],\) is considered, where \(\alpha\in (0,1)\), \(g\in C[0,T]\) and the kernel k is continuous in \(S\times {\mathbb{R}}\) with \(S=\{(t,s): 0\leq s\leq t\leq T\}\) and satisfies a Lipschitz condition with respect to the third variable. For the numerical solution of these equations a class of methods depending on some parameters is introduced. Some bounds on the parameters are determined so that the corresponding methods have infinite stability intervals.