Abstract:
Some methods with memory for solving nonlinear equations are
designed from known methods without memory. We increase
the convergence order from 4 to 6 by using a free parameter accelerator by Newton's interpolatory polynomial of the third degree. So, its efficiency
index is even better than optimal sixteenth-order methods without
memory. Dynamical behavior on low-degree polynomials is analyzed,
highly improving the stability properties of the original schemes.
Numerical test problems are given to prove its competitiveness with
methods of the same class.
Key Words: Iterative methods, R-order, Steffensen-like methods with memory,
computational efficiency, Herzberger’s matrix, stability, basin of attraction.
2010 Mathematics Subject Classification: Primary: 65H05,
Secondary: 65D05, 37M99.
Download the paper in pdf format here.
