Work

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

Year: 2024

Type: article

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.

Source: Mathematics

DOI: 10.3390/math12233655

Authors: Shuai Wang, Haomiao Xian, Tao Liu, Stanford Shateyi

Institutions: Changchun Guanghua University, Beijing Normal University, Northeastern University, University of Venda

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: Natural Science Foundation of Hebei Province, Fundamental Research Funds for the Central Universities, Division of Graduate Education