Skip to main content
SpringerLink
Log in

Metodo di euler e ricerca delle radici di una equazione

  • Published:
CALCOLO Aims and scope Submit manuscript

Abstract

In this paper the problem of the research of the roots of an equation is resolved by means of the integration of a differential equation with Euler's method. The aim is to increase the convergence region of the iterative process until it coincides with the region of the asymptotical stability of the roots for the differential equations used. Different algrothms are obtained, some of which are unknown in the literature. Also a class of functions, the entire functions of 0,1 genus is found for which is guaranteed the convergence on a pre-established root.

Sommario

In questa nota il problema della ricerca di radici di una equazione viene risolto mediante l'integrazione con il metodo di Eulero di una equazione differenziale. Lo scopo è quello di aumentare il dominio di convergenza dei procedimenti iterativi fino a farlo coincidere col dominio di asintotica stabilità della radice per l'equazione diflerenziale usata. Si ottengono diversi algoritmi, alcuni dei quali non noti in letteratura. Si dà anche una classe di funzioni, le funzioni intere di genus 0,1, per la quele è garantita la convergenza ad una radice prefissata.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Bibliografia

  1. D. F. Davidenko,A new method of numerical solution of systems of nonlinear equations, Dokl. Akad., Nauk SSSR88 (1953), 601–602.

    MATH  MathSciNet  Google Scholar 

  2. H. K. Kuiken,Determination of the intersection points of two plane curves by means of differential equations, Comm. ACM.11, (1968), 502–506.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. H. Meyer,On solving nonlinear equations with one parameter operator inbedding, SIAM J. N. A.5 (1968), 739–752.

    Article  MATH  Google Scholar 

  4. P. T. Boggs,The solution of nonlinear systems of equations by A-stable integration techniques, SIAM J. N. A. (1971), 767–785.

  5. F. H. Branin,Widely convergent method for finding multiple solutions of simultaneous nonlinear equations, IBM J. Res. Devel.16 (1972), 504–522.

    Article  MATH  MathSciNet  Google Scholar 

  6. I. Galligani, D. Trigiante,Numerical methods for solving large algebraic systems, IAC Pubblicazioni serie III, n. 98.

  7. E. Isaacson, H. B. Keller,Analysis of numerical methods, (1966),J. Wiley, New York.

    MATH  Google Scholar 

  8. J. D. Lambert,Computational methods in ordinary differential equations, (1973),J. Wiley, New York.

    MATH  Google Scholar 

  9. J. D. Lambert,Two unconventional classes of methods for stiff systems, in R. A. Willoughby Stiff. Differential systems, (1974), pag. 171–185, Plenum Press, N. Y.

    Google Scholar 

  10. R. P. Boas,Entire functions (1954), Plunum Press, N. Y.

    MATH  Google Scholar 

  11. H. J. Stetter,Economical global error estimation, in R. A. Willoughby, Stiff Differential Systems, (1974), pagg. 245–258, Plenum Press, N. Y.

    Google Scholar 

  12. W. Hahn,Stability of motion, (1967) Springer, Berlin.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Matematica, Università di Bari, Palazzo Ateneo, Bari

    G. Di Lena & D. Trigiante

  2. IBM Centro Ricerche, Via Cardassi, 3, Bari

    D. Trigiante

Authors
  1. G. Di Lena
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Trigiante
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Di Lena, G., Trigiante, D. Metodo di euler e ricerca delle radici di una equazione. Calcolo 13, 377–396 (1976). https://doi.org/10.1007/BF02576631

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02576631

Search

Navigation