Abstract
In this paper, we develop an optimal family of two-step single root finding methods with order 4. Furthermore, we modify these numerical schemes to locate all nonlinear real and complex roots at the same time. The order of convergence is demonstrated using convergence analysis to be four for a single root-finding technique and for families of parallel computer methods. Numerical test examples reveal that the developed parallel techniques achieve superior stability and consistency compared to existing approaches.
Keywords
Convergence (economics)
Nonlinear system
Consistency (knowledge bases)
Stability (learning theory)
Parallel algorithm
Numerical stability
Numerical analysis
Computer science
Algorithm
Subject Areas
Iterative Methods for Nonlinear Equations
·Numerical Analysis ·Physical Sciences
Numerical Methods and Algorithms
·Computational Theory and Mathematics ·Physical Sciences
Advanced Optimization Algorithms Research
·Numerical Analysis ·Physical Sciences