Nordsieck representation of high order predictor-corrector Obreshkov methods and their implementation

Document Type : Research Paper

Authors

Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

Abstract

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method is discussed by providing Nordsieck representation of the method and preparing an starting procedure, an estimate for local truncation error and a formula for changing stepsize. Efficiency and capability of the method are shown by some numerical experiments.

Keywords


Volume 7, Issue 1
January 2019
Pages 16-27
  • Receive Date: 13 November 2017
  • Revise Date: 05 February 2018
  • Accept Date: 23 October 2018
  • First Publish Date: 01 January 2019