Numerical Solution of Nonlinear Problems with Multiple Roots Using Derivative-Free Algorithms
نویسندگان
چکیده
In the study of systems’ dynamics presence symmetry dramatically reduces complexity, while in chemistry, plays a central role analysis structure, bonding, and spectroscopy molecules. more general context, principle equivalence, local symmetry, dictated gravity, space-time itself. certain instances, especially we end up having to deal with an equation multiple roots. A variety optimal methods have been proposed literature for roots known multiplicity, all which need derivative evaluations formulations. However, literature, without derivatives are few. Motivated by this feature, here present novel family fourth-order do not use any derivative. The scheme new iterative consists two steps, namely Traub-Steffensen Traub-Steffensen-like iterations weight factor. According Kung-Traub hypothesis, algorithms satisfy optimality criterion. Taylor’s series expansion is used examine order convergence. We also demonstrate application real-life problems, i.e., Van der Waals problem, Manning Planck law radiation Kepler’s problem. Furthermore, performance comparisons shown that given derivative-free competitive existing require information.
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ژورنال
عنوان ژورنال: Symmetry
سال: 2023
ISSN: ['0865-4824', '2226-1877']
DOI: https://doi.org/10.3390/sym15061249