On the construction of numerical iterative schemes of any order of convergence for solving nonlinear systems of equations

This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using the method proposed in this paper. A test case is conducted n...

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Bibliographic Details
Published in:INCAS bulletin 2018-06, Vol.10 (2), p.207-220
Main Authors: Stefan, HOTHAZIE, Camelia, MUNTEANU, Mihaela, NASTASE
Format: Article
Language:English
Subjects:
Computer algebra
Construction methods
Convergence
Iterative methods
iterative schemes
Mathematical analysis
nonlinear algebraic equations
Nonlinear equations
Nonlinear systems
numerical applications
order of convergence
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Summary:This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using the method proposed in this paper. A test case is conducted numerically for the second and third order of convergence using a computer algebra system called Maxima. The code used is listed at the end of the test case.
ISSN:2066-8201
2247-4528
DOI:10.13111/2066-8201.2018.10.2.19