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: 328

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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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

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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

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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Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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