On the twostep secant type method for solving nonlinear equations(in Ukrainian) 

Author 
s shakhno@franko.lviv.ua
Ivan Franko National University of Lviv

Abstract 
In the paper the twostep secant type method for solving nonlinear operator equations under
the generalized Lipschitz condition for divided difference is investigated. The convergence order
and the radius of the convergence domain of the iterative process are established.

Keywords 
nonlinear operator equation; iterative process; Lipschitz condition

Reference 
1. Bartish M.Ya. About one iterative method of solving functional equations// Dop. AN URSR. Ser. A.
1968. V. 5. P. 387391. (in Ukrainian)
2. Bartish M.Ya., Shcherbyna Yu.M. About one difference method of solving operator equations// Dop. AN URSR. Ser. A. 1972. V.7. P. 579582. (in Ukrainian) 3. Kantorovich L.V., Akilov G.P. Functional analysis. Moscow: Nauka, 1984. (in Russian) 4. Shakhno S.M. On an iterative algorithm with superquadratic convergence for solving nonlinear operator equations// J. Comp. App. Math. 2009. V.231. P. 222235. 5. Shakhno S.M. Secant method under the generalized Lipschitz conditions for the firstorder divided differences// Mathematical bulletin of the Shevchenko scientific society. 2007. V.4. P. 296305. (in Ukrainian) 6. Shakhno S.M. Convergence of the twostep Newton type method for solving of nonlinear equations under the generalized Lipschitz conditions// Physicomathematical modelling and informational technologies. 2012. V.16. Π. 163172. (in Ukrainian) 7. Shakhno S.M., Grab S.I., Yarmola H.P. Twoparametric secant type methods for solving nonlinear equations// Visnyk of the Lviv University. Series Applied Mathematics and Computer Science. 2009. V.15. P. 117127. (in Ukrainian) 8. Wang X. Convergence of Newtons method and uniquiness of the solution of equations in Banach space// IMA Journal of Numerical Analysis. 2000. V.20. P. 123134. 9. Werner W. Uber ein Verfahren der Ordnung $1+\sqrt{2} $ zur Nullstellenbestimmung// Numer. Math. 1979. V.32. P. 333342. 
Pages 
8488

Volume 
42

Issue 
1

Year 
2014

Journal 
Matematychni Studii

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