Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations
In this paper we propose a generating function method for constructing new two and three-point iterations with p (p = 4, 8) order of convergence. This approach allows us to derive a new family of optimal order iterative methods that include well known methods as special cases. Necessary and sufficie...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
|
| Series: | EPJ Web of Conferences |
| Online Access: | https://doi.org/10.1051/epjconf/201817303024 |
| _version_ | 1818717186156396544 |
|---|---|
| author | Zhanlav Tugal Chuluunbaatar Ochbadrakh Ulziibayar Vandandoo |
| author_facet | Zhanlav Tugal Chuluunbaatar Ochbadrakh Ulziibayar Vandandoo |
| author_sort | Zhanlav Tugal |
| collection | DOAJ |
| description | In this paper we propose a generating function method for constructing new two and three-point iterations with p (p = 4, 8) order of convergence. This approach allows us to derive a new family of optimal order iterative methods that include well known methods as special cases. Necessary and sufficient conditions for p-th (p = 4, 8) order convergence of the proposed iterations are given in terms of parameters τn and αn. We also propose some generating functions for τn and αn. We develop a unified representation of all optimal eighth-order methods. The order of convergence of the proposed methods is confirmed by numerical experiments. |
| first_indexed | 2024-12-17T19:31:09Z |
| format | Article |
| id | doaj.art-2ac5fbe22fd34380b6c48ec2ea8b6af2 |
| institution | Directory Open Access Journal |
| issn | 2100-014X |
| language | English |
| last_indexed | 2024-12-17T19:31:09Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | EPJ Web of Conferences |
| spelling | doaj.art-2ac5fbe22fd34380b6c48ec2ea8b6af22022-12-21T21:35:15ZengEDP SciencesEPJ Web of Conferences2100-014X2018-01-011730302410.1051/epjconf/201817303024epjconf_mmcp2018_03024Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear EquationsZhanlav TugalChuluunbaatar OchbadrakhUlziibayar VandandooIn this paper we propose a generating function method for constructing new two and three-point iterations with p (p = 4, 8) order of convergence. This approach allows us to derive a new family of optimal order iterative methods that include well known methods as special cases. Necessary and sufficient conditions for p-th (p = 4, 8) order convergence of the proposed iterations are given in terms of parameters τn and αn. We also propose some generating functions for τn and αn. We develop a unified representation of all optimal eighth-order methods. The order of convergence of the proposed methods is confirmed by numerical experiments.https://doi.org/10.1051/epjconf/201817303024 |
| spellingShingle | Zhanlav Tugal Chuluunbaatar Ochbadrakh Ulziibayar Vandandoo Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations EPJ Web of Conferences |
| title | Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations |
| title_full | Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations |
| title_fullStr | Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations |
| title_full_unstemmed | Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations |
| title_short | Generating Function Approach to the Derivation of Higher-Order Iterative Methods for Solving Nonlinear Equations |
| title_sort | generating function approach to the derivation of higher order iterative methods for solving nonlinear equations |
| url | https://doi.org/10.1051/epjconf/201817303024 |
| work_keys_str_mv | AT zhanlavtugal generatingfunctionapproachtothederivationofhigherorderiterativemethodsforsolvingnonlinearequations AT chuluunbaatarochbadrakh generatingfunctionapproachtothederivationofhigherorderiterativemethodsforsolvingnonlinearequations AT ulziibayarvandandoo generatingfunctionapproachtothederivationofhigherorderiterativemethodsforsolvingnonlinearequations |