Variants of Steffensen-Secant method and applications

DOI10.1016/j.amc.2010.04.058zbMath1200.65036OpenAlexW2025986106MaRDI QIDQ988595

Li Zhang, Peng Zhao, Quan Zheng, Wen Chao Ma

Publication date: 18 August 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.04.058

zbMATH Keywords

Newton's methodnumerical examplesefficiencyboundary value problemsnonlinear equationderivative-freemultiple shooting methodsimple/multiple rootSteffensen-secant methodssuper cubic convergence

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical computation of solutions to single equations (65H05) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (11)

A new accelerating technique applied to a variant of Cordero-Torregrosa method ⋮ Some optimal iterative methods and their with memory variants ⋮ On an Aitken-Newton type method ⋮ Iterative methods for multiple roots with memory using self-accelerating technique ⋮ A Steffensen type method of two steps in Banach spaces with applications ⋮ An optimal biparametric multipoint family and its self-acceleration with memory for solving nonlinear equations ⋮ A family of high order derivative-free iterative methods for solving root-finding problems ⋮ A family of fourth-order Steffensen-type methods with the applications on solving nonlinear ODEs ⋮ An optimal Steffensen-type family for solving nonlinear equations ⋮ Rapidly convergent Steffensen-based methods for unconstrained optimization ⋮ A family of Newton-type iterative methods using some special self-accelerating parameters

Cites Work

• A new method of secant-like for nonlinear equations
• A two-step Steffensen's method under modified convergence conditions
• An analysis of the properties of the variants of Newton's method with third order convergence
• Recurrence relations for rational cubic methods. I: The Halley method
• Steffensen type methods for solving non-linear equations
• The secant method and divided differences Hölder continuous
• On Newton-type methods for multiple roots with cubic convergence
• A Steffensen-like method and its higher-order variants
• A Steffensen's type method in Banach spaces with applications on boundary-value problems
• A family of Chebyshev-Halley type methods in Banach spaces
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