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

	Nordsieck representation of high order predictor-corrector Obreshkov methods and their implementation
Computational Methods for Differential Equations
مقاله 2، دوره 7، شماره 1، فروردین 2019، صفحه 16-27 اصل مقاله (2.54 M)
نوع مقاله: Research Paper
نویسندگان
Behnaz Talebi؛ Ali Abdi^*
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
چکیده
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.
کلیدواژه‌ها
PEC methods؛ Adams methods؛ Nordsieck representation؛ Local error estimation؛ Variable stepsize

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