Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems
Alicia Cordero, Eva G. Villalba, Juan R. Torregrosa, Paula Triguero‐Navarro
Abstract
A new parametric class of iterative schemes for solving nonlinear systems is designed. The third- or fourth-order convergence, depending on the values of the parameter being proven. The analysis of the dynamical behavior of this class in the context of scalar nonlinear equations is presented. This study gives us important information about the stability and reliability of the members of the family. The numerical results obtained by applying different elements of the family for solving the Hammerstein integral equation and the Fisher’s equation confirm the theoretical results.
Topics & Concepts
Parametric statisticsNonlinear systemScalar (mathematics)Applied mathematicsMathematicsConvergence (economics)Stability (learning theory)Class (philosophy)Iterative methodContext (archaeology)Mathematical optimizationComputer sciencePhysicsMachine learningEconomicsEconomic growthPaleontologyStatisticsArtificial intelligenceGeometryQuantum mechanicsBiologyIterative Methods for Nonlinear EquationsAdvanced Optimization Algorithms ResearchFractional Differential Equations Solutions