A fast algorithm to solve systems of nonlinear equations

A new HSS-based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved. Spectral properties of the new method are investigated. Performance profile for the new scheme is computed and compared with HSS algorithm. Besides, by a numerical example in wh...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 354; pp. 242 - 258
Main Authors Amiri, Abdolreza, Cordero, Alicia, Darvishi, Mohammad Taghi, Torregrosa, Juan R.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2019
Subjects
Iterative method
Jacobian free scheme
Newton method
Newton-GPSS method
Newton–HSS method
Nonlinear systems
Newton–HSS method
Iterative method
Jacobian free scheme
Newton-GPSS method
Nonlinear systems
Newton method
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ISSN0377-0427
1879-1778
1879-1778
DOI10.1016/j.cam.2018.03.048

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Summary:A new HSS-based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved. Spectral properties of the new method are investigated. Performance profile for the new scheme is computed and compared with HSS algorithm. Besides, by a numerical example in which a two-dimensional nonlinear convection–diffusion equation is solved, we compare the new method and the Newton–HSS method. Numerical results show that the new scheme solves the problem faster than the Newton–HSS scheme in terms of CPU-time and number of iterations. Moreover, the application of the new method is found to be fast, reliable, flexible, accurate, and has small CPU time.
ISSN:0377-0427
1879-1778
1879-1778
DOI:10.1016/j.cam.2018.03.048