In this paper, a numerical collocation method is developed for solving linear and nonlinear Volterra integral equations of the second kind. The method is based on the approximation of the (exact) solution by a superposition of sigmoidal functions and allows one to solve a large class of integral equations having either continuous or $L^p$ solutions. Special computational advantages are obtained using unit step functions, and analytical approximations of the solution are also at hand. The numerical errors are discussed, and a priori as well as a posteriori estimates are derived for them. Numerical examples are given for the purpose of illustration.
"Solving Volterra integral equations of the second kind by sigmoidal functions approximation." J. Integral Equations Applications 25 (2) 193 - 222, SUMMER 2013. https://doi.org/10.1216/JIE-2013-25-2-193