On efficient fractional caputo-Type simultaneous scheme for finding all roots of polynomial equations with biomedical engineering applications

Shams, Mudassir; KAUSAR, Nasreen; Samaniego, Cuauhtemoc; Agarwal, Praveen; Ahmed, Shams; Momani, Shaher

doi:10.1142/s0218348x23400753

On efficient fractional caputo-Type simultaneous scheme for finding all roots of polynomial equations with biomedical engineering applications

Shams M., KAUSAR N., Samaniego C., Agarwal P., Ahmed S. F., Momani S.

Fractals, vol.31, no.4, 2023 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 31 Issue: 4
Publication Date: 2023
Doi Number: 10.1142/s0218348x23400753
Journal Name: Fractals
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Compendex, INSPEC, zbMATH, DIALNET, Civil Engineering Abstracts
Keywords: Caputo-Type Derivative, Computational Efficiency, Computer Algorithm, Error Graph, Optimal Order, Simultaneous Methods
Yıldız Technical University Affiliated: Yes

Abstract

This research paper introduces a novel fractional Caputo-Type simultaneous method for finding all simple and multiple roots of polynomial equations. Without any additional polynomial and derivative evaluations using suitable correction, the order of convergence of the basic Aberth-Ehrlich simultaneous method has been increased from three to α + 3. In terms of accuracy, residual graph, computational efficiency and computation CPU time, the newly proposed families of simultaneous methods outperforms existing methods in numerical applications.