Local convergence for multistep high order methods under weak conditions

Volume 47 / 2020

Ioannis K. Argyros, Ramandeep Behl, Daniel González, S. S. Motsa Applicationes Mathematicae 47 (2020), 293-304 MSC: 65G99, 65H10, 47J25, 47J05, 65D10, 65D99. DOI: 10.4064/am2374-1-2019 Published online: 12 October 2020

Abstract

We present a local convergence analysis for an eighth-order convergent method in order to find a solution of a nonlinear equation in a Banach space setting. In contrast to the earlier studies using hypotheses up to the seventh Fréchet derivative, we use only hypotheses on the first-order Fréchet derivative and Lipschitz constants. This way, we not only expand the applicability of these methods but also propose a computable radius of convergence for these methods. Finally, concrete numerical examples demonstrate that our results apply to nonlinear equations not covered before.

Authors

  • Ioannis K. ArgyrosDepartment of Mathematics Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
    ORCID: 0000-0002-9189-9298
  • Ramandeep BehlSchool of Mathematics
    Statistics and Computer Sciences
    University of KwaZulu-Natal
    Private Bag X01, Scottsville 3209
    Pietermaritzburg, South Africa
    ORCID: 0000-0003-1505-8945
  • Daniel GonzálezEscuela de Ciencias Físicas y Matemáticas
    Universidad de Las Américas
    Quito 170125, Ecuador
    ORCID: 0000-0001-5282-7251
    e-mail
  • S. S. MotsaSchool of Mathematics
    Statistics and Computer Sciences
    University of KwaZulu-Natal
    Private Bag X01, Scottsville 3209
    Pietermaritzburg, South Africa

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