Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval | Zendy

Taher Lotfi | Zendy; Fazlollah Soleymani | Zendy; Somayeh Sharifi | Zendy; Stanford Shateyi | Zendy; F. Khaksar Haghani | Zendy

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Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval

Author(s) -

Taher Lotfi,

Fazlollah Soleymani,

Somayeh Sharifi,

Stanford Shateyi,

F. Khaksar Haghani

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/601205

Subject(s) - simple (philosophy) , interval (graph theory) , convergence (economics) , mathematics , algorithm , nonlinear system , fractal , computer science , iterative method , rate of convergence , order (exchange) , key (lock) , mathematical optimization , mathematical analysis , philosophy , physics , computer security , epistemology , combinatorics , quantum mechanics , finance , economics , economic growth

Two new families of multipoint without memory iterative methods with eighth- and sixteenth-orders are constructed using the symbolic software Mathematica. The key idea in constructing such methods is based on producing some generic suitable functions to reduce the functional evaluations and increase the order of convergence along the computational efficiency. Again by applying Mathematica, we design a hybrid algorithm to capture all the simple real solutions of nonlinear equations in an interval. The application of the new schemes in producing fractal pictures is also furnished

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