A General Three-Step Class of Optimal Iterations for Nonlinear Equations | Zendy

Fazlollah Soleymani | Zendy; S. Karimi Vanani | Zendy; Abtin Afghani | Zendy

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A General Three-Step Class of Optimal Iterations for Nonlinear Equations

Author(s) -

Fazlollah Soleymani,

S. Karimi Vanani,

Abtin Afghani

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/469512

Subject(s) - class (philosophy) , convergence (economics) , nonlinear system , root (linguistics) , mathematics , order (exchange) , function (biology) , root finding algorithm , mathematical optimization , computer science , artificial intelligence , linguistics , philosophy , physics , finance , quantum mechanics , evolutionary biology , economics , biology , economic growth

Many of the engineering problems are reduced to solve a nonlinear equation numerically, and as a result, an especial attention to suggest efficient and accurate root solvers is given in literature. Inspired and motivated by the research going on in this area, this paper establishes an efficient general class of root solvers, where per computing step, three evaluations of the function and one evaluation of the first-order derivative are used to achieve the optimal order of convergence eight. The without-memory methods from the developed class possess the optimal efficiency index 1.682. In order to show the applicability and validity of the class, some numerical examples are discussed

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