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Doubly-accelerated Steffensen’s methods with memory and their applications on solving nonlinear ODEs. (English) Zbl 1275.65027

The authors present a parametric accelerated Steffensen’s method with memory and its error equation for solving nonlinear equations. Three doubly-accelerated Steffensen’s methods with memory are derived from the parametric accelerated Steffensen’s method. All the proposed methods use two new evaluations of the function per step. Each of the doubly-accelerated Steffensen’s methods uses six or seven multiplications/divisions per iteration. Some numerical examples are provided to illustrate the efficiency of the proposed methods.

MSC:

65H05 Numerical computation of solutions to single equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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