On the convergence of two-step Newton-type methods of high efficiency index

Volume 36 / 2009

Ioannis K. Argyros, Saïd Hilout Applicationes Mathematicae 36 (2009), 465-499 MSC: 65H10, 65G99, 65J15, 47H17, 49M15. DOI: 10.4064/am36-4-6


We introduce a new idea of recurrent functions to provide a new semilocal convergence analysis for two-step Newton-type methods of high efficiency index. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar type, and a differential equation containing a Green's kernel are also provided.


  • Ioannis K. ArgyrosDepartment of Mathematics
    Cameron University
    Lawton, OK 73505, U.S.A.
  • Saïd HiloutLaboratoire de Mathématiques et Applications
    Université de Poitiers
    Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179
    86962 Futuroscope Chasseneuil Cedex, France

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