A new type of recurrence relations for the Secant method.

  1. Hernández, M.A. 1
  2. Rubio, M.J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Zeitschrift:
International Journal of Computer Mathematics

ISSN: 0020-7160

Datum der Publikation: 1999

Ausgabe: 72

Nummer: 4

Seiten: 477-490

Art: Artikel

SCOPUS: 2-s2.0-0012605421 WoS: WOS:000083869000006 GOOGLE SCHOLAR

Andere Publikationen in: International Journal of Computer Mathematics

Zusammenfassung

We apply the Secant method to solve nonlinear operator equations in Banach spaces. We establish a Newton - Kantorovich convergence theorem using a new system of recurrence relations and give an explicit expression for the a priori error bounds. Moreover, we apply our results to the numerical resolution of a nonlinear boundary value problem of second order and improve the error bounds obtained by other authors.