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Russia Yekaterinburg
Section Mathematics
Title One specification of Steffensen's method for solving nonlinear operator equations
Author(-s) Yumanova I.F.a
Affiliations Ural Federal Universitya
Abstract We consider an analogue of Steffensen's method for solving nonlinear operator equations. The proposed method is a two-step iterative process. We study the convergence of the proposed method, prove the uniqueness of the solution and find the order of convergence. The proposed method uses no derivative operators. The convergence order is greater than that in Newton's method and some generalizations of the method of chords and Aitken-Steffensen's method. The method is applied to some test systems of nonlinear equations and the problem of curves intersection which are defined implicitly as solutions of differential equations. Numerical results are compared with the results obtained by Newton's method, the modified Newton method, and modifications of Wegstein's and Aitken's methods which were proposed by the author in previous works.
Keywords nonlinear operator equation, Steffensen's method, Newton's method, problem of the intersection curves
UDC 519.615.5, 519.642.6
MSC 45G10, 65J15
DOI 10.20537/vm160411
Received 30 October 2016
Language Russian
Citation Yumanova I.F. One specification of Steffensen's method for solving nonlinear operator equations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 4, pp. 579-590.
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