Cordero, A.; Reyes, J.A.; Torregrosa, J.R.; Vassileva, M.P. Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations. Axioms2024, 13, 34.
Cordero, A.; Reyes, J.A.; Torregrosa, J.R.; Vassileva, M.P. Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations. Axioms 2024, 13, 34.
Cordero, A.; Reyes, J.A.; Torregrosa, J.R.; Vassileva, M.P. Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations. Axioms2024, 13, 34.
Cordero, A.; Reyes, J.A.; Torregrosa, J.R.; Vassileva, M.P. Stability Analysis of a New Fourth-Order Optimal Iterative Scheme for Nonlinear Equations. Axioms 2024, 13, 34.
Abstract
In this paper, we present a new parametric class of optimal fourth-order iterative methods to estimate the solutions of nonlinear equations. After the convergence analysis, we study the stability of this class by using the tools of complex discrete dynamics. This allows us to select those elements of the class with lower dependence on initial estimations. We verify by means of numerical tests that the stable members on quadratic polynomials perform better than the unstable ones, when applied to other non-polynomial functions. We also compare the performance of the best elements of the family with known methods, such as the schemes by Newton or Chun, among others, showing robust and stable behaviour.
Computer Science and Mathematics, Applied Mathematics
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