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

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.

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
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