@article{Ma2024, 
author = {Wei Ma and Ming Zhao and Jiaxin Li},
title = {A multi-step Ulm-Chebyshev-like method for solving nonlinear operator equations},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {28623-28642},
keywords = {nonlinear equation, multi-step, Ulm-Chebyshev-like method, R-convergence rate 4},
url = {https://www.sciopen.com/article/10.3934/math.20241389},
doi = {10.3934/math.20241389},
abstract = {In this paper, based on the Ulm-Chebyshev iterative procedure, we present a multi-step Ulm-Chebyshev-like method to solve systems of nonlinear equations  F(x)=0,   {yn=xn−BnF(xn),zn=yn−BnF(yn),xn+1=zn−BnF(zn),B¯n=2Bn−BnAn+1Bn,Bn+1=B¯n+B¯n(2I−An+1B¯n)(I−An+1B¯n),n=0,1,2,…,where  An+1 is an approximation of the derivative  F′(xn+1). This method does not contain inverse operators in its expression, and does not require computing Jacobian matrices for solving Jacobian equations. We have proved that the multi-step Ulm-Chebyshev-like method converges locally to the solution with  R-convergence rate 4 under appropriate conditions. Some applications are given, compared with other existing methods, where the most important features of the method are shown.}
}