The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

Hirotada Okawa*, Kotaro Fujisawa, Yu Yamamoto, Ryosuke Hirai, Nobutoshi Yasutake, Hiroki Nagakura, Shoichi Yamada

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a new class of method for solving nonlinear systems of equations, which, among other things, has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extension to the Newton-Raphson (NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.

Original languageEnglish
Pages (from-to)157-172
Number of pages16
JournalApplied Numerical Mathematics
Volume183
DOIs
Publication statusPublished - 2023 Jan

Keywords

  • Iterative methods
  • Partial differential equations
  • System of nonlinear equations

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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