Efficient Nyström-type method for the solution of highly oscillatory Volterra integral equations of the second kind. [PDF]
PLoS ONE, 2023 Highly oscillatory Volterra integral equations are frequently encountered in engineering applications. The Nyström-type method is an important numerical approach for solving such problems.
Qinghua Wu, Mengjun Sun
doaj +2 more sources
Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice [PDF]
HeliyonIn this paper, a connection is established between the Jones polynomial of generalized weaving knots of type W(3,n,m) and the Chebyshev polynomial of the first kind.
Mark E. AlSukaiti, Nafaa Chbili
doaj +2 more sources
New equivalent resistance formula of $$m\times n$$ rectangular resistor network represented by Chebyshev polynomials [PDF]
Scientific ReportsIn the process of exploring the field of circuits, obtaining the exact solution of the equivalent resistance between two nodes in a resistor network has become an important problem.
Ru Wang +4 more
doaj +2 more sources
Chebyshev polynomials of the first kind and the univariate Lommel function: Integral representations
Open MathematicsThis study investigates a number of integrals possessing products of different indices of the univariate Lommel function, sμ,ν(a){s}_{\mu ,\nu }\left(a), with various elementary and special functions.
da Fonseca Carlos M. +2 more
doaj +2 more sources
An Efficient Collocation Method for the Numerical Solutions of the Pantograph-Type Volterra Hammerstein Integral Equations and its Convergence Analysis [PDF]
Computational Algorithms and Numerical Dimensions, 2022 In this work, we consider a collocation method for solving the pantograph-type Volterra Hammerstein integral equations based on the first kind Chebyshev polynomials. We use the Lagrange interpolating polynomial to approximate the solution.
Hashem Saberi Najafi +2 more
doaj +1 more source
Unified Convergence Analysis of Chebyshev–Halley Methods for Multiple Polynomial Zeros
Mathematics, 2022 In this paper, we establish two local convergence theorems that provide initial conditions and error estimates to guarantee the Q-convergence of an extended version of Chebyshev–Halley family of iterative methods for multiple polynomial zeros due to ...
Stoil I. Ivanov
doaj +1 more source
On Berman's phenomenon for (0,1,2) Hermite-Fejér interpolation
Journal of Numerical Analysis and Approximation Theory, 2019 Given \(f\in C[-1,1]\) and \(n\) points (nodes) in \([-1,1]\), the Hermite-Fejer interpolation (HFI) polynomial is the polynomial of degree at most \(2n-1\) which agrees with \(f\) and has zero derivative at each of the nodes. In 1916, L.
Graeme J Byrne, Simon Jeffrey Smith
doaj +7 more sources
Journal of Mathematics, 2022 In the paper, we study the upper bound estimation of the Lebesgue constant of the bivariate Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the second kind on the square −1,12. And, we prove that the growth
Juan Liu, Laiyi Zhu
doaj +1 more source
Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials [PDF]
Mathematics, 2018 In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here, the coefficients involve terminating hypergeometric functions
Taekyun Kim +3 more
openaire +2 more sources
Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials [PDF]
Mathematical Problems in Engineering, 2015 We use the combinatorial method and algebraic manipulations to obtain several interesting identities involving the power sums of the derivative of the first kind Chebyshev polynomials. This solved an open problem proposed by Li (2015).
Wang, Tingting, Zhang, Han
openaire +1 more source