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Solving Nonlinear Equation Systems via a Steffensen-Type Higher-Order Method with Memory.

Solving Nonlinear Equation Systems via a Steffensen-Type Higher-Order Method with Memory.

Authors :
Wang, Shuai
Xian, Haomiao
Liu, Tao
Shateyi, Stanford
Source :
Mathematics (2227-7390); Dec2024, Vol. 12 Issue 23, p3655, 14p
Publication Year :
2024

Abstract

This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subsequently extend it to a method with memory. The resulting order is 5 + 2 , utilizing the identical number of functional evaluations as the solver without memory, thereby demonstrating a higher computational index of efficiency. Finally, we illustrate the advantages of the proposed scheme with memory through various test problems. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
22277390
Volume :
12
Issue :
23
Database :
Complementary Index
Journal :
Mathematics (2227-7390)
Publication Type :
Academic Journal
Accession number :
181656284
Full Text :
https://doi.org/10.3390/math12233655