The convergence of the Euler's method

Authors

  • Raluca Anamaria Sălăjan (Pomian) Vasile Alecsandri Secondary School, Baia Mare, Romania

DOI:

https://doi.org/10.33993/jnaat391-922

Keywords:

Euler's method, fixed point, one-point iteration method
Abstract views: 332

Abstract

In this article we study the Euler's iterative method. For this method we give a global theorem of convergence. In the last section of the paper we give a numerical example which illustrates the result exposed in this work.

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References

Amat, S., Busquier, S. and Plaza, S., Review of some iterative root-finding methods from a dynamical point of view, Scientia, Series A: Mathematical Sciences, 10, pp. 3-35, 2004.

Osada, N., A one parameter family of locally quartically convergent zero-finding methods, J. Comput. Appl. Math., 205, pp. 116-128, 2007, https://doi.org/10.1016/j.cam.2006.04.045 DOI: https://doi.org/10.1016/j.cam.2006.04.045

Păvăloiu, I., Sur les procedées itérative à un order élevé de convergence, Mathématica, 12(35), no. 2, pp. 309-324, 1970.

Păvăloiu, I. and Pop, N., Interpolare şi aplicaţii , Editura Risoprint, Cluj-Napoca, 2005 (in Romanian).

Petković, L. D., Petković, M. S. and Ziviković, D., Hansen-Patrick's family is of Laguerre's type, Novi Sad J. Math., 33, no. 1, pp. 109-115, 2003.

Petrović, M., Tričković, S. and Herceg, D., Higher order Euler-like methods, Novi Sad J. Math., 28, no. 3, pp. 129-136, 1998.

Varona, J., Graphic and numerical comparison between iterative methods, The Mathematical Intelligencer, 24, no. 1, pp. 37-46, 2002, https://doi.org/10.1007/bf03025310 DOI: https://doi.org/10.1007/BF03025310

Ye, X. and Li, C., Convergence of the family of the deformed Euler-Halley iterations under the Hölder condition of the second derivative, Journal of Computational and Applied Mathematics, 194, pp. 294-308, 2006, https://doi.org/10.1016/j.cam.2005.07.019 DOI: https://doi.org/10.1016/j.cam.2005.07.019

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Published

2010-02-01

How to Cite

Sălăjan (Pomian), R. A. (2010). The convergence of the Euler’s method. Rev. Anal. Numér. Théor. Approx., 39(1), 87–92. https://doi.org/10.33993/jnaat391-922

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