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

Shuai Wang, Haomiao Xian, Tao Liu and Stanford Shateyi ()
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Shuai Wang: Foundation Department, Changchun Guanghua University, Changchun 130033, China
Haomiao Xian: School of Statistics, Beijing Normal University, Beijing 100875, China
Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Stanford Shateyi: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2024, vol. 12, issue 23, 1-14

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.

Keywords: with memory; Steffensen-type; higher-order methods; fractal attraction basins; efficiency index (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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