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

Revue:
International Journal of Computer Mathematics

ISSN: 0020-7160

Année de publication: 1999

Volumen: 72

Número: 4

Pages: 477-490

Type: Article

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

D'autres publications dans: International Journal of Computer Mathematics

Résumé

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.