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 Forruque; Momani, Shaher (WORLD SCIENTIFIC PUBL CO PTE LTD, 2023)
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 a + 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.
Keywords: Optimal Order; Simultaneous Methods; Caputo-Type Derivative; Error Graph; Computational Efficiency; Computer Algorithm; ITERATION METHODS; ZEROS; CONVERGENCE; Mathematics; Science & Technology - Other Topics