Higher-Order Root-Finding Algorithms and Their Basins of Attraction
Amir Naseem, M. A. Rehman, Thabet Abdeljawad
Abstract
In this paper, we proposed and analyzed three new root-finding algorithms for solving nonlinear equations in one variable. We derive these algorithms with the help of variational iteration technique. We discuss the convergence criteria of these newly developed algorithms. The dominance of the proposed algorithms is illustrated by solving several test examples and comparing them with other well-known existing iterative methods in the literature. In the end, we present the basins of attraction using some complex polynomials of different degrees to observe the fractal behavior and dynamical aspects of the proposed algorithms.
Topics & Concepts
MathematicsConvergence (economics)AlgorithmRoot (linguistics)AttractionNonlinear systemVariable (mathematics)Applied mathematicsMathematical optimizationMathematical analysisEconomic growthEconomicsLinguisticsPhysicsQuantum mechanicsPhilosophyIterative Methods for Nonlinear EquationsFractional Differential Equations SolutionsMathematical and Theoretical Analysis