SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION
The article is about the analysis of semi-local convergence of a seventh-order iterative method used for finding the roots of a nonlinear equation in Banach spaces. In this article, the imposed hypotheses is amiable than the well-known Lipschitz and Hölder continuity conditions. The R-order converge...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University Constantin Brancusi of Targu-Jiu
2020-04-01
|
| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v15/p15_12.pdf |
| Summary: | The article is about the analysis of semi-local convergence of a seventh-order iterative method used for finding the roots of a nonlinear equation in Banach spaces. In this article, the imposed hypotheses is amiable than the well-known Lipschitz and Hölder continuity conditions. The R-order convergence of the considered scheme is proved to be at least 4+3q. An approximate apriori error bound for this method is also elaborated and the domain of existence and uniqueness of the solution in the convergence theorem. Two numerical illustrations have been worked out to exhibit the virtue of the developed theory. |
|---|---|
| ISSN: | 1843-7265 1842-6298 |