A class of numerical methods for autonomous initial value problems

Abstract

In this paper we introduce a class of explicit numerical methods for approximating the solutions of scalar initial value problems for first order differential equations, using a nonlinear interpolation formula. We show that the methods generated in this way can be identified as explicit Runge-Kutta methods and we analyze some particular cases. Finally, numerical examples are provided.

Authors

Flavius Patrulescu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

initial value problem; stability region; convergence order; local truncation error

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Cite this paper as:

F. Pătrulescu, A class of numerical methods for autonomous initial value problems, Rev. Anal. Numer. Theor. Approx., vol. 41, no. 1 (2012), pp. 82-92

About this paper

Publisher Name

Publishing House of the Romanian Academy (Editura Academiei Române), Cluj-Napoca

Print ISSN

1222-9024

Online ISSN

2457-8126/e

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References

Section 2
References

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[2] Crouzeix, A.L. Mignot, Analyse numerique des equations differentielles, Masson, Paris (1989).
[3] D. Lambert, Numerical Methods for Ordinary Differential Systems. The Initial Value Problem, John Wiley & Sons, Chichester (1990).
[4] Patrulescu, A Numerical Method for the Solution of an Autonomous Initial Value Problem, Carpathian J. Math., 28, no. 2 (2012), 289-296.
[5] Pavaloiu, On an approximation formula, Rev. Anal. Numer. Theor. Approx.,  26, no. 1-2 (1997), 179-183.
[6] Ralston, Runge-Kutta Methods with Minimum Error Bounds, Math. Comp.,16, no. 80 (1962), 431-437.
[7] F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1964).

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