High Order Three-Steps Newton Raphson-like Schemes for Solving Nonlinear Equation Systems

DOI

10.2991/acsr.k.220202.021How to use a DOI?

Keywords

Nonlinear equation systems; Newton-Raphson method; Newton-cotes open form

Abstract

This study proposes several new 3-steps schemes based on the Newton-Raphson method for solving non-linear equation systems. The proposed schemes are analysed and formulated based on the Newton-Raphson method and the Newton-cotes open form numerical integration method. In general, the schemes can be considered as a predictor and corrector principles. In the first and the third steps, the Newton-Raphson method is applied. Furthermore, Newton-cotes Open Form numerical integration modification is operated in the second step of the proposed schemes. The convergence analysis of the proposed schemes is given. It shows that the proposed scheme provides the 8^th order of convergence. The performance of the proposed schemes is compared and assessed with several numerical examples.

Copyright

© 2022 The Authors. Published by Atlantis Press International B.V.

Open Access

This is an open access article under the CC BY-NC license.

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TY  - CONF
AU  - Rizki Multazamil Fatahillah
AU  - M Ziaul Arif
AU  - Rusli Hidayat
AU  - Kusbudiono
AU  - Ikhsanul Halikin
PY  - 2022
DA  - 2022/02/08
TI  - High Order Three-Steps Newton Raphson-like Schemes for Solving Nonlinear Equation Systems
BT  - Proceedings of the  International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
PB  - Atlantis Press
SP  - 101
EP  - 108
SN  - 2352-538X
UR  - https://doi.org/10.2991/acsr.k.220202.021
DO  - 10.2991/acsr.k.220202.021
ID  - Fatahillah2022
ER  -