ON EFFICIENT FRACTIONAL CAPUTO-TYPE SIMULTANEOUS SCHEME FOR FINDING ALL ROOTS OF POLYNOMIAL EQUATIONS WITH BIOMEDICAL ENGINEERING APPLICATIONS
Mudassir Shams, Nasreen Kausar, Cuauhtémoc Samaniego, Praveen Agarwal, Shams Forruque Ahmed, Shaher Momani
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 [Formula: see text]. 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.
Topics & Concepts
Convergence (economics)ComputationResidualPolynomialApplied mathematicsMathematicsScheme (mathematics)GraphType (biology)Mathematical optimizationComputer scienceAlgorithmDiscrete mathematicsMathematical analysisBiologyEconomic growthEcologyEconomicsIterative Methods for Nonlinear EquationsFractional Differential Equations SolutionsAdvanced Optimization Algorithms Research