Comparative analysis of numerical solutions of ODEs with initial value problems using improved euler methods


Authors

DOI:

https://doi.org/10.22517/23447214.24892

Keywords:

Interpolation

Abstract

This document contains a detailed comparison between the initial numerical solution methods of ordinary differential equations, which start from the Euler method approach, which is based on the solution of differential equations by the Taylor method, the others two methods to be compared are improvements of this method, that of Euler, and they are the method of Heun, and the method of the midpoint. It will be observed from the solution of test differential equations its respective error with respect to the analytical solution, obtaining an error index dictated by the mean square error EMC. Through this document we will know the best numerical approximation to the analytical solution of the different PVI (initial value problems) raised, also fixing a solution pattern for certain problems, that is, the appropriate method for each type of problem will be stipulated.

Downloads

Download data is not yet available.

References

[1]. M. Kline and M. Martínez, “El pensamiento matemático de la Antigüedad a nuestros días”, Alianza Editorial, Madrid, España, 1992.

[2]. J. E. Napoles Valdes, “Un siglo de teoría cualitativa de ecuaciones diferenciales”, Lecturas Matemáticas, Universidad de la Cuenca del Plata, Argentina, 2004.

[3]. S. C. Chapra and R. P. Canale, “Métodos numéricos para

ingenieros”, McGraw-Hill, México, 2007.

[4]. J. D. Faires, R. L. Burden and P. J. P. Escolano, “Métodos numéricos”, Thomson-Paraninfo, España, 2007.

[5]. A. Quarteroni, R. Sacco, and F. Saleri, “Numerical mathematics”,Springer Science & Business Media, Berlin, 2010. doi:10.1007/b98885

[6]. Ledanois, J. M. (2000). Métodos numéricos aplicados eningeniería (No. 517/M59).

[7]. J. H. Mathews and K. D. Fink, “Métodos numéricos con Matlab”,Pearson, Madrid, 2000.

[8]. K. E. Atkinson, and W. Han, “Elementary numerical analysis”,Wiley, New York, 2005

Downloads

Published

2021-09-30

How to Cite

Devia Narvaez, D. M., Mesa, F., & Correa Vélez, G. . (2021). Comparative analysis of numerical solutions of ODEs with initial value problems using improved euler methods. Scientia Et Technica, 26(03), 391–397. https://doi.org/10.22517/23447214.24892

Issue

Section

Ciencias Básicas