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.


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