A class of numerical methods for autonomous initial value problems

Authors

  • Flavius Olimpiu Pătrulescu Tiberiu Popoviciu Institute of Numerical Analysis, Romania

DOI:

https://doi.org/10.33993/jnaat411-970

Keywords:

initial value problem, stability region, convergence order, local truncation error
Abstract views: 310

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.

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References

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J.D. Lambert, Numerical Methods for Ordinary Differential Systems-The Initial Value Problem, John Wiley & Sons, 1990.

F. Pătrulescu, A numerical method for the solution of an autonomous initial value problem, Carpathian J. Math., 28, no. 2, pp. 289-296, 2012. DOI: https://doi.org/10.37193/CJM.2012.02.05

I. Păvăloiu, On an approxiation formula, Rev. Anal. Numér. Théor. Approx., 26, no. 1--2, pp. 179-183, 1997, http://ictp.acad.ro/jnaat/journal/article/view/1997-vol26-nos1-2-art23

A. Ralston, Runge-Kutta methods with minimum error bounds, Math. Comp., 16, no. 80, pp. 431-437, 1962. https://doi.org/10.1090/s0025-5718-1962-0150954-0 DOI: https://doi.org/10.1090/S0025-5718-1962-0150954-0

J. F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964.

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Published

2012-01-01

How to Cite

Pătrulescu, F. O. (2012). A class of numerical methods for autonomous initial value problems. Rev. Anal. Numér. Théor. Approx., 41(1), 82–92. https://doi.org/10.33993/jnaat411-970

Issue

Vol. 41 No. 1 (2012)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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