Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels

Authors

  • S. G. Solodkii

Abstract

For the Volterra equations with analytic kernels, we establish the exact power order of complexity of their approximate solutions and show that the optimal power order is realized by the method of simple iterations based on the use of information in the form of the values of kernels and free terms at certain points. In addition, for the Volterra equations with infinitely differentiable kernels, we determine the minimal order of the error of direct methods and construct a method which realizes this order.

Published

25.11.1994

Issue

Section

Research articles

How to Cite

Solodkii, S. G. “Optimization of Algorithms for the Approximate Solution of the Volterra Equations With Infinitely Differentiable Kernels”. Ukrains’kyi Matematychnyi Zhurnal, vol. 46, no. 11, Nov. 1994, pp. 1534–1545, https://umj.imath.kiev.ua/index.php/umj/article/view/5592.