A new variable step size algorithm for Cauchy problem

In this study, we have obtained a step size strategy based on Picard–Lindelöf 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–Lindelöf theorem and error analysis and obtains approximate solutions. The strategy and algorithm are modifications of the strategy and algorithm in [G. Çelik Kızılkan, K. Aydın, Step size strategy based on error analysis, Selcuk University Science and Art Faculty Journal of Science 25 (2005) 79–86 (in Turkish)].