Generalization of the bisection method and its applications in nonlinear equations

Gulshan, Ghazala; Budak, HÜSEYİN; Hussain, Rashida; Sadiq, Asad

doi:10.1186/s13662-023-03765-5

Generalization of the bisection method and its applications in nonlinear equations

Gulshan G., Budak H., Hussain R., Sadiq A.

ADVANCES IN CONTINUOUS AND DISCRETE MODELS, cilt.2023, sa.1, 2023 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 2023 Sayı: 1
Basım Tarihi: 2023
Doi Numarası: 10.1186/s13662-023-03765-5
Dergi Adı: ADVANCES IN CONTINUOUS AND DISCRETE MODELS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Kocaeli Üniversitesi Adresli: Hayır

Özet

The aim of the current work is to generalize the well-known bisection method using quantum calculus approach. The results for different values of quantum parameter q are analyzed, and the rate of convergence for each q ? (0,1) is also determined. Some physical problems in engineering are resolved using the QBM technique for various values of the quantum parameter q up to three iterations to examine the validity of the method. Furthermore, it is proven that QBM is always convergent and that for each interval there exists q ? (0,1) for which the first approximation of root coincides with the precise solution of the problem.