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, cilt.31, sa.4, 2023 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 31 Sayı: 4
Basım Tarihi: 2023
Doi Numarası: 10.1142/s0218348x23400753
Dergi Adı: Fractals
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Compendex, INSPEC, zbMATH, DIALNET, Civil Engineering Abstracts
Anahtar Kelimeler: Caputo-Type Derivative, Computational Efficiency, Computer Algorithm, Error Graph, Optimal Order, Simultaneous Methods
Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.