Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems
Xiaofeng Wang, Yingfanghua Jin, Yali Zhao
Abstract
Some Kurchatov-type accelerating parameters are used to construct some derivative-free iterative methods with memory for solving nonlinear systems. New iterative methods are developed from an initial scheme without memory with order of convergence three. New methods have the convergence order 2+5≈4.236 and 5, respectively. The application of new methods can solve standard nonlinear systems and nonlinear ordinary differential equations (ODEs) in numerical experiments. Numerical results support the theoretical results.
Topics & Concepts
Nonlinear systemConvergence (economics)Derivative (finance)Iterative methodOdeApplied mathematicsComputer scienceType (biology)Ordinary differential equationScheme (mathematics)Local convergenceConstruct (python library)MathematicsAlgorithmDifferential equationMathematical analysisPhysicsFinancial economicsBiologyQuantum mechanicsEcologyProgramming languageEconomic growthEconomicsIterative Methods for Nonlinear EquationsAdvanced Optimization Algorithms ResearchMatrix Theory and Algorithms