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Homotopy method for solving

Homotopy method for solving. fuzzy nonlinear 'equations. 8'. Abbasband~. anc.R. Ezzati. Abstract. In this paper, ,ve introduce tr,e numerical solution for a fuzzy. llonlinear systems by homotopy met::od. The fuzzy quantities are pre-.

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Homotopy method for solving

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  1. Homotopy method for solving fuzzy nonlinear 'equations 8'. Abbasband~. anc.R. Ezzati . Abstract. In this paper, ,ve introduce tr,e numerical solution for a fuzzy llonlinear systems by homotopy met::od. The fuzzy quantities are pre- sented ill parametric form. Some numerical illustrations are given to sho,v the efficiency of algorithms. . M.S.C. 2000: 3-1AI2. 65105. Key words: homotopy and continuation method. Rung-Kutta method, Fuzzy parametric form. Fuzzy nonlinear equation~. 1 Introduction In recent years. the homotopy method h~ bee:l used by scientists. Recently. the ap- plications of homotop:' theory among sciel1~:~t~ "".ereappe<ued [13. 1-1.1.5.18. 19]. and the homotop:' theory becomes a po,verful :lli1t::ematical tool, ,vhen it is successfully coupled ,vith perturbation theory. [1, 2. 16. Ii:. The numerical solution of a algebrc1ic non:inear equation like F(x) = 0, arises quite often in engineering and the natural5ciences. :\Ian:. engineering design problems that must satisf:. specified constraint as a nonline<1requalities or inequalities. One of the major applic<1tions of fuzzy number ar:thmetic is nonlinear equations ,vhose parameters are all or partially represented b:' fuzz:. numbers [4, 11. 21]. Standard cmcuytical techniques like Buckley and Q',: method. [.5,6, 7, 8], can not suitable for solving the equations such as (i) ax-l+bx3+cx2+dx+e=f, (ii) x + cos(x) = g, where x. a. b. c, d, e,f and Q are fuzz:' n1.::"!lber~.\\"e therefore need to develop the numeric<1lmethods to find the roots of tl:~se equations, in general as F(x) = O. The Ne,vton's method for solving a fuzz:' no:,,!inear equation is considered in [3]. The advantage of the Newton's method is it'" speed of convergence once a sufficiently accurate approximation is kno,vn. A ,veakness of this method is that an accurate initial approximation to the solution is needed to ensure convergence. In section 2, ,ve recall some fund<1mentalresult~ of fuzzy numbers. In section 3, we propose Homotopy and Continuation :\Iethod for solving fuzzy nonlinear systems. 11:1; section '1, ,ve illustrate some exc1mplesand conclusions in the last section. A~plied Sciences,Vol.8, 2006, pp. 1-7. @ Balkan Society of Geometers, Geometry Balk£'.n Pre"s 2006.

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