A new variable step size algorithm for Cauchy problem

Gülnur Çelı̇k Kızılkan

doi:10.1016/j.amc.2006.06.035

A new variable step size algorithm for Cauchy problem

2006-12-01

2

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AI

G

Gülnur Çelı̇k Kızılkan *

K

Kemal Aydın

DOI：10.1016/j.amc.2006.06.035

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Abstract

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In this study, we have obtained a step size strategy based on Picard-Lindelof theorem and error analysis for the numeric integration of Cauchy problems in a region where the solutions of Cauchy problems exist and are unique. We have given an algorithm which calculates step size based on Picard-Lindelof theorem and error analysis and obtains approximate solutions. The strategy and algorithm are modifications of the strategy and algorithm in [G. Celik Kizilkan, K. Aydin, Step size strategy based on error analysis, Selcuk University Science and Art Faculty Journal of Science 25 (2005) 79-86 (in Turkish)]. (c) 2006 Elsevier Inc. All rights reserved.

Keywords:

variable step size

Picard-Lindelof theorem

numerical integration

step size strategy

error analysis

A new variable step size algorithm for Cauchy problem

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