Comparison and successive iteration of approximate solution of ordinary differential equations with initial conditions by the new modified Krasnoselskii iteration method

Bildik N., Bakir Y., Mutlu A.

SCIENTIA IRANICA, vol.20, no.6, pp.1792-1804, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 6
  • Publication Date: 2013
  • Journal Name: SCIENTIA IRANICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1792-1804
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we used the Picard successive iteration method and the new modified Krasnoselskii iteration method in order to solve different types of ordinary linear differential equations having initial conditions. By applying the new modified Krasnoselskii iteration method, not only do we obtain the approximate solutions for the problem, but also establish the corresponding iterative schemes Finally, it is shown that the accuracy of the new iteration method (called the new modified Krasnoselskii iteration method) is substantially improved by employing variable steps which adjust themselves to the solution of the differential equation. (C) 2013 Sharif University of Technology. All rights reserved.