TY - JOUR
T1 - The W4 method
T2 - A new multi-dimensional root-finding scheme for nonlinear systems of equations
AU - Okawa, Hirotada
AU - Fujisawa, Kotaro
AU - Yamamoto, Yu
AU - Hirai, Ryosuke
AU - Yasutake, Nobutoshi
AU - Nagakura, Hiroki
AU - Yamada, Shoichi
N1 - Funding Information:
We would like to thank K.-i Maeda for helpful comments. We are grateful to Y. Eriguchi for valuable comments on the preliminary draft. H. O. is grateful to Z. Pelgrims for reproducing our result. This work was supported by JSPS KAKENHI Grant Number 16K17708 , 16H03986 , 17K18792 , 20K03953 , 20K14512 . R. H. was supported by JSPS overseas research fellowship No. 29-514 . K. F was supported by JSPS postdoctoral fellowships No. 16J10223 . H. N. was partially supported at Caltech through NSF award No. TCAN AST-1333520 and DOE SciDAC4 Grant DE-SC0018297 (subaward 00009650). S. Y. is supported by the Institute for Advanced Theoretical and Experimental Physics , Waseda University and the Waseda University Grant for Special Research Projects (project number: 2020C-273 , 2021C-197 , 2022C-140 ).
Publisher Copyright:
© 2022 The Authors
PY - 2023/1
Y1 - 2023/1
N2 - 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.
AB - 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.
KW - Iterative methods
KW - Partial differential equations
KW - System of nonlinear equations
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U2 - 10.1016/j.apnum.2022.08.019
DO - 10.1016/j.apnum.2022.08.019
M3 - Article
AN - SCOPUS:85138101476
SN - 0168-9274
VL - 183
SP - 157
EP - 172
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -