Abstract
In this paper, we present a first order local regularization method for solving ill-posed Volterra equations with ν-smoothing kernels, and establish stability and convergence of the method for all values of ν∈N. The method is an improvement of one whose numerical performance is shown to erode at ν=4 and whose convergence theory is uncertain once ν>4. We describe numerical implementation of the fast sequential algorithm associated with the method and provide a new scheme to approximate the initial condition. Numerical examples illustrate our theoretical results, particularly the method's stability in the case ν=4 and higher.