Use of fractional calculus to avoid divergence in Newton-like solver for solving one-dimensional nonlinear polynomial-based models
[ X ]
Tarih
2025-04
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier BV
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
There are many different fields of study where nonlinear polynomial-based models arise and need to be solved, making the study of root-finding iterative solvers an important topic of research. Our goal was to use the two most significant fractional differential operators, Caputo and Riemann–Liouville, and an existing time-efficient three-step Newton-like iterative solver to address the growing interest in fractional calculus. The classical solver is preserved alongside a damping term created within it that tends to 1 as the fractional order α approaches 1. The solvers’ local and semi-local convergence are investigated, and the stability trade-off with convergence speed is discussed at length. The suggested fractional-order solvers are tested on a number of nonlinear one-dimensional polynomial-based problems that come up in image processing, mechanical design, and civil engineering, such as beam deflection; and many more.
Açıklama
Anahtar Kelimeler
Basins of attraction, Fractional order derivative, Local and semilocal analysis, Stability
Kaynak
Communications in Nonlinear Science and Numerical Simulation
WoS Q Değeri
Scopus Q Değeri
Q1
Cilt
143
Sayı
Künye
Qureshi, S., Soomro, A., Argyros, I. K., Gdawiec, K., Akgül, A., & Alquran, M. (2025). Use of fractional calculus to avoid divergence in newton-like solver for solving one-dimensional nonlinear polynomial-based models. Communications in Nonlinear Science and Numerical Simulation, 108631.