Hybrid Operators for Approximating Nonsmooth Functions and Applications on Volterra Integral Equations with Weakly Singular Kernels. (2nd January 2023)

• Record Type: Journal Article
• Authors: Buranay, S. C.; Özarslan, M. A.; Falahhesar, S. S.
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 1(2023)
• Page Start: 36
• Page End: 63
• Publication Date: 2023-01-02
• Subjects: Asymptotic rate of convergence -- hybrid operators -- regularization -- singular kernel -- Volterra integral equations; 41A36 -- 41A25 -- 45D05 -- 65D15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2150642
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This research concerns some theoretical and numerical aspects of hybrid positive linear operators for approximating continuous functions on [ 0, 1 ] that have unbounded derivatives at the initial point. These operators are defined by using Modified Bernstein–Kantorovich operators K n, α, where n is positive integer, α > 0 is a fixed constant and reduces to the classical Bernstein–Kantorivich operators when α = 1 . To show the importance and the applicability of the given hybrid operators we develop an algorithm which implements them for solving the second kind linear Volterra integral equations with weakly singular kernels. Furthermore, applications are also performed on first kind integral equations, by utilizing regularization. Eventually, it is shown that the numerical realization of the given algorithm is easy and computationally efficient and gives accurate approximations to nonsmooth solutions.