Abstract
We introduce a new faster King-Werner-type derivative-free method for solving nonlinear equations. The local as well as semi-local convergence analysis is presented under weak center Lipschitz and Lipschitz conditions. The convergence order as well as the convergence radii are also provided. The radii are compared to the corresponding ones from similar methods. Numerical examples further validate the theoretical results.
Highlights
We present the local convergence analysis of KWTM based on scalar parameters and functions
We present some numerical examples
The number of iterations (n) needed to the solution applying the stopping criterion ( xn+1 − xn + F (xn) ) < 10−200 is 10
Summary
We present the local convergence analysis of method (2.10) using the preceding notation and conditions whereas and X, Y are Banach spaces until otherwise specified. Sequence {xn} generated by Secant method (2.25) for x−1, x0 ∈ B(x∗, r∗)-{x∗} is well defined in B(x∗, r∗), remains in B(x∗, r∗) for each n = 0, 1, 2, . It was shown in [1,2] that under conditions (2.11) and (2.12) the radius of convergence for Newton’s method xn+1 = xn − F ′(xn)−1F (xn). We present the local convergence analysis of KWTM based on scalar parameters and functions. The induction for (2.42) and (2.43) is completed analysis if x0, y0, x1, y1 are replaced by xm, ym, xm+1, ym+1 in the preceding estimates, respectively.
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