Extended convergence analysis of Newton-Potra solver for equations

Ioannis Argyros; Stepan M. Shakhno; Yurii Shunkin; Halyna Yarmola

doi:10.33993/jnaat492-1186

Authors

Ioannis Argyros Cameron University, USA https://orcid.org/0000-0002-9189-9298
Stepan M. Shakhno Ivan Franko National University of Lviv, Ukraine https://orcid.org/0000-0002-3845-6260
Yurii Shunkin Ivan Franko National University of Lviv, Ukraine
Halyna Yarmola Ivan Franko National University of Lviv, Ukraine https://orcid.org/0000-0002-8986-2509

DOI:

https://doi.org/10.33993/jnaat492-1186

Keywords:

nonlinear equation, nondifferentiable operator, local and semi-local convergence, order of convergence, divided difference

Abstract views: 247

Abstract

In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839.... The radius of the convergence ball and convergence order of the investigated solver are determined in an earlier paper. Modifications of previous conditions leads to extended convergence domain. These advantages are obtained under the same computational effort.

Numerical experiments are carried out on the test examples with nondifferentiable operator.

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