A smoothed projection method for singular, nonlinear Volterra equations

Abstract

A modified Galerkin method previously used to approximate the solution of nonlinear Volterra integral equations of the second kind with smooth kernels is generalized to include such equations with singular, monotone kernels of convolution type. Several singular kernel approximations are considered, including positive convolution operators and integral splines. The main results relating to the original integral equation supply error estimates resulting from using the kernel approximations and an approximating system of ordinary differential equations.