ON TWO-STEP PARALLEL COMPUTER ALGORITHM FOR ALL NONLINEAR EQUATIONS ROOTS WITH ENGINEERING APPLICATIONS

Shams M., KAUSAR N., Agarwal P., Alqahtani N. A., Jeelani M. B.

Fractals, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2026
  • Doi Number: 10.1142/s0218348x26400141
  • Journal Name: Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
  • Keywords: Computational Time, Convergence, Fractal, Percentage Computational Cost, Polynomial, Simultaneous Methods
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we develop an optimal family of two-step single root finding methods with order 4. Furthermore, we modify these numerical schemes to locate all nonlinear real and complex roots at the same time. The order of convergence is demonstrated using convergence analysis to be four for a single root-finding technique and for families of parallel computer methods. Numerical test examples reveal that the developed parallel techniques achieve superior stability and consistency compared to existing approaches.