New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns

Ramandeep Behl, Alicia Cordero, Juan R. Torregrosa and Ali Saleh Alshomrani
Additional contact information
Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Alicia Cordero: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 Valencia, Spain
Juan R. Torregrosa: Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 Valencia, Spain
Ali Saleh Alshomrani: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2018, vol. 6, issue 12, 1-17

Abstract: In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature.

Keywords: nonlinear equations; local convergence analysis; order of convergence; Newton’s method; multi-point iterative methods; computational order of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/6/12/296/pdf (application/pdf)
https://www.mdpi.com/2227-7390/6/12/296/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:6:y:2018:i:12:p:296-:d:187042

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().