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

Author

Listed:
  • Shuai Wang

    (Foundation Department, Changchun Guanghua University, Changchun 130033, China)

  • Haomiao Xian

    (School of Statistics, Beijing Normal University, Beijing 100875, China
    IT Department, Sichuan Rural Commercial United Bank, Chengdu 610000, 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)

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.

Suggested Citation

  • Shuai Wang & Haomiao Xian & Tao Liu & Stanford Shateyi, 2024. "Solving Nonlinear Equation Systems via a Steffensen-Type Higher-Order Method with Memory," Mathematics, MDPI, vol. 12(23), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3655-:d:1526728
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