An Efficient Iterative Method Based on Two-Stage Splitting Methods to Solve Weakly Nonlinear Systems

Abdolreza Amiri, Mohammad Taghi Darvishi, Alicia Cordero and Juan Ramón Torregrosa
Additional contact information
Abdolreza Amiri: Department of Mathematics, Razi University, Kermanshah 67149, Iran
Mohammad Taghi Darvishi: Department of Mathematics, Razi University, Kermanshah 67149, Iran
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Juan Ramón Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Mathematics, 2019, vol. 7, issue 9, 1-17

Abstract: In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem for this method. In addition, it is shown that any faster and less time-consuming two-stage splitting method that satisfies the convergence theorem can be replaced instead of the HSS inner iterations. Numerical results, such as CPU time, show the robustness of our new method. This method is easy, fast and convenient with an accurate solution.

Keywords: system of nonlinear equations; Newton method; Newton-HSS method; nonlinear HSS-like method; Picard-HSS method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/9/815/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/9/815/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:9:p:815-:d:263730

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().