An improved first order local regularization method for ill-posed Volterra equations

摘要

In this paper, we present a first order local regularization method for solving ill-posed Volterra equations with nu-smoothing kernels, and establish stability and convergence of the method for all values of nu is an element of N. The method is an improvement of one whose numerical performance is shown to erode at nu = 4 and whose convergence theory is uncertain once nu > 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 nu = 4 and higher. (C) 2019 Published by Elsevier Inc.