Global error estimation of linear multistep methods through the Runge-Kutta methods

Iranian Journal of Numerical Analysis and Optimization

مقاله 4، دوره 6، شماره 2 - شماره پیاپی 10، آذر 2016، صفحه 99-120   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v6i2.35736

نویسنده

J. Farzi^*

Department of Mathematics, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran.

چکیده

In this paper, we study the global truncation error of the linear multistep methods (LMM) in terms of local truncation error of the corresponding Runge-Kutta schemes. The key idea is the representation of LMM with a corresponding Runge-Kutta method. For this, we need to consider the multiple step of a linear multistep method as a single step in the corresponding Runge-Kutta method. Therefore, the global error estimation of a LMM through the Runge-Kutta method will be provided. In this estimation, we do not take into account the effects of roundoff errors. The numerical illustrations show the accuracy and efficiency of the given estimation.

کلیدواژه‌ها

Linear multistep methods؛ Runge-Kutta methods؛ Local trun- cation error؛ Global error؛ Error estimation

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