ON EFFICIENT FRACTIONAL CAPUTO-TYPE SIMULTANEOUS SCHEME FOR FINDING ALL ROOTS OF POLYNOMIAL EQUATIONS WITH BIOMEDICAL ENGINEERING APPLICATIONS

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.

Automated summary

This research paper presents a novel fractional Caputo-type simultaneous method that efficiently determines all simple and multiple roots of polynomial equations. By incorporating suitable corrections, the order of convergence of the basic Aberth-Ehrlich simultaneous method has been improved from three to a + 3. In terms of accuracy, residual graph, computational efficiency, and computation CPU time, the newly proposed family of simultaneous methods surpasses existing methods in numerical applications.