nondifferentiable operator
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scholarly journals Two-Step Solver for Nonlinear Equations

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 128 ◽  
Author(s):  
Ioannis Argyros ◽  
Stepan Shakhno ◽  
Halyna Yarmola
Keyword(s):  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Semilocal Convergence ◽  
Numerical Example ◽  
Weaker Conditions ◽  
Theoretical Results ◽  
Nondifferentiable Operator

In this paper we present a two-step solver for nonlinear equations with a nondifferentiable operator. This method is based on two methods of order of convergence 1 + 2 . We study the local and a semilocal convergence using weaker conditions in order to extend the applicability of the solver. Finally, we present the numerical example that confirms the theoretical results.

scholarly journals On the two-step method for solving nonlinear equations with nondifferentiable operator

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 617-618 ◽  
Author(s):  
Stepan Shakhno ◽  
Halyna Yarmola
Keyword(s):  
Nonlinear Equations ◽  
Step Method ◽  
Nondifferentiable Operator

scholarly journals ON SOME PROJECTION METHODS FOR THE SOLUTION OF NONLINEAR EQUATIONS WITH NONDIFFERENTIABLE OPERATORS

1993 ◽  
Vol 24 (1) ◽  
pp. 1-7
Author(s):  
IOANNIS K. ARGYROS
Keyword(s):  
Banach Space ◽  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
Operator Equation ◽  
Dimensional Space ◽  
Projection Methods ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
Nondifferentiable Operator

We consider a nonlinear equation with a nondifferentiable operator in a Banach space. We approximate a solution of the nonlinear equation using an iteration, whose iterates can be obtained by solving a certain operator equation in a finite dimensional space.  

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