A variant of Steffensen’s method of fourth-order convergence and its applications. (English) Zbl 1208.65064

Liu, Zhongli; Zheng, Quan; Zhao, Peng

Appl. Math. Comput. 216, No. 7, 1978-1983 (2010).

A variant of Steffensen’s method is presented, which uses divided differences instead of derivatives. Fourth-order convergence is proved. Numerical tests are given for nonlinear algebraic and ordinary differential equations.

Reviewer: János Karátson (Budapest)

MSC:

65H05	Numerical computation of solutions to single equations
34A34	Nonlinear ordinary differential equations and systems
65L20	Stability and convergence of numerical methods for ordinary differential equations
65L12	Finite difference and finite volume methods for ordinary differential equations

Keywords:

nonlinear equations; Newton’s method; Steffensen’s method; derivative free; fourth-order convergence; numerical examples

References:

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