TY - JOUR
T1 - Semilocal convergence of Chebyshev Kurchatov type methods for non-differentiable operators
AU - Yadav, Sonia
AU - Singh, Sukhjit
AU - Badoni, R. P.
AU - Kumar, Ajay
AU - Singh, Mehakpreet
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/9/15
Y1 - 2024/9/15
N2 - In this study, the new semilocal convergence for the family of Chebyshev Kurchatov type methods is proposed under weaker conditions. The convergence analysis demands conditions on the initial approximation, auxiliary point, and the underlying operator (Argyros et al. (2017) [10]). By utilizing the notion of auxiliary point in convergence conditions, the convergence domains are obtained where the existing results are not applicable. The theoretical results are validated using numerical examples, such as nonlinear PDE and mixed Hammerstein type integral equations originating in biology, vehicular traffic theory, and queuing theory, to determine the applicability of the proposed framework. The numerical testing shows that the new approach performed better (accurately and converge faster) than Steffensen's method, Chebyshev type methods and two step secant method.
AB - In this study, the new semilocal convergence for the family of Chebyshev Kurchatov type methods is proposed under weaker conditions. The convergence analysis demands conditions on the initial approximation, auxiliary point, and the underlying operator (Argyros et al. (2017) [10]). By utilizing the notion of auxiliary point in convergence conditions, the convergence domains are obtained where the existing results are not applicable. The theoretical results are validated using numerical examples, such as nonlinear PDE and mixed Hammerstein type integral equations originating in biology, vehicular traffic theory, and queuing theory, to determine the applicability of the proposed framework. The numerical testing shows that the new approach performed better (accurately and converge faster) than Steffensen's method, Chebyshev type methods and two step secant method.
KW - Chebyshev Kurchatov type methods
KW - Convergence balls
KW - Integral equations
KW - Recurrence relations
KW - Semilocal convergence
UR - http://www.scopus.com/inward/record.url?scp=85199146417&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2024.07.003
DO - 10.1016/j.camwa.2024.07.003
M3 - Article
AN - SCOPUS:85199146417
SN - 0898-1221
VL - 170
SP - 275
EP - 281
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
ER -