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A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior

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dc.contributor.author Tassaddiq, Asifa
dc.contributor.author Qureshi, Sania
dc.contributor.author Soomro, Amanullah
dc.contributor.author Hincal, Evren
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Shaikh, Asif Ali
dc.date.accessioned 2022-03-01T11:58:45Z
dc.date.available 2022-03-01T11:58:45Z
dc.date.issued 2021-12
dc.identifier.citation Tassaddiq, Asifa...et al. (2021). "A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior", Fractal and Fractional, Vol. 5, No. 4. tr_TR
dc.identifier.issn 2504-3110
dc.identifier.uri http://hdl.handle.net/20.500.12416/5059
dc.description.abstract There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within the scientific literature, we attempt to devise a new nonlinear three-step method with tenth-order convergence while using six functional evaluations (three functions and three first-order derivatives) per iteration. The method has an efficiency index of about 1.4678, which is higher than most optimal methods. Convergence analysis for single and systems of nonlinear equations is also carried out. The same is verified with the approximated computational order of convergence in the absence of an exact solution. To observe the global fractal behavior of the proposed method, different types of complex functions are considered under basins of attraction. When compared with various well-known methods, it is observed that the proposed method achieves prespecified tolerance in the minimum number of iterations while assuming different initial guesses. Nonlinear models include those employed in science and engineering, including chemical, electrical, biochemical, geometrical, and meteorological models. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.3390/fractalfract5040204 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Nonlinear Models tr_TR
dc.subject Efficiency Index tr_TR
dc.subject Computational Cost tr_TR
dc.subject Halley’s Method tr_TR
dc.subject Basin of Attraction tr_TR
dc.subject Computational Order of Convergence tr_TR
dc.title A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior tr_TR
dc.type article tr_TR
dc.relation.journal Fractal and Fractional tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 5 tr_TR
dc.identifier.issue 4 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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