Modified Newton-EHS method for solving nonlinear problems with complex symmetric Jacobian matrices

Lv Zhang; Qingbiao Wu; Lv Zhang; Qingbiao Wu

doi:10.3934/math.20231236

AIMS Mathematics

2023, Volume 8, Issue 10: 24233-24253. doi: 10.3934/math.20231236

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Research article

Modified Newton-EHS method for solving nonlinear problems with complex symmetric Jacobian matrices

Lv Zhang ,
Qingbiao Wu ^,

School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310058, China

Received: 09 May 2023 Revised: 08 July 2023 Accepted: 27 July 2023 Published: 14 August 2023
MSC : 65F10, 65F50, 65H10

This manuscript is devoted to the study of numerical methods for a class of nonlinear problems. Instead of the standard Newton method, an efficient nonlinear solver is suggested to be used, and it is referred to as the Newton-EHS method, where "EHS" stands for Euler-extrapolated Hermitian-skew-Hermitian splitting. We construct this modified Newton-EHS method by utilizing a modified Newton method as the outer iteration and the EHS method as the inner iteration. Furthermore, we give the derivations of the local and semilocal convergence properties of the proposed method under the Hölder condition. Finally, in order to show the feasibility and validity of our new method, we compare it with some other iterative methods in two numerical examples.
- large sparse nonlinear systems,
- iterative method,
- Newton's method,
- complex symmetric Jacobian matrix,
- convergence analysis
Citation: Lv Zhang, Qingbiao Wu. Modified Newton-EHS method for solving nonlinear problems with complex symmetric Jacobian matrices[J]. AIMS Mathematics, 2023, 8(10): 24233-24253. doi: 10.3934/math.20231236

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Abstract

This manuscript is devoted to the study of numerical methods for a class of nonlinear problems. Instead of the standard Newton method, an efficient nonlinear solver is suggested to be used, and it is referred to as the Newton-EHS method, where "EHS" stands for Euler-extrapolated Hermitian-skew-Hermitian splitting. We construct this modified Newton-EHS method by utilizing a modified Newton method as the outer iteration and the EHS method as the inner iteration. Furthermore, we give the derivations of the local and semilocal convergence properties of the proposed method under the Hölder condition. Finally, in order to show the feasibility and validity of our new method, we compare it with some other iterative methods in two numerical examples.

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