JOURNAL ARTICLE

SSPH-Newton Iterative Method for Solving Nonlinear Equations.

  • Published In: International Journal of Computational Methods, 2024, v. 21, n. 7. P. 1 1 of 3

  • Database: Applied Science & Technology Source Ultimate 2 of 3

  • Authored By: Guan, Xuehao; Wang, Rui 3 of 3

Abstract

In this paper, a new kernel approximation is constructed based on the basic principle of kernel approximation of meshless symmetric smooth particle hydrodynamics (SSPH) method. The first derivative is calculated by constructing a symmetric matrix through Taylor series expansion. Replacing the derivative of Newton's method, the SSPH-Newton iterative method for solving nonlinear equations is proposed. The advantage of this method is that it does not need to evaluate the derivative and overcomes the shortcomings of Newton's method. The quadratic convergence of the new method is proved. Numerical and application examples show that the method has the same accuracy as Newton method, the efficiency index is higher than Newton method, and the calculation amount is lower than Newton method. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Computational Methods. 2024/09, Vol. 21, Issue 7, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:02198762
  • DOI:10.1142/S021987622450021X
  • Accession Number:179770709
  • Copyright Statement:Copyright of International Journal of Computational Methods is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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