Results 21 to 30 of about 183 (122)
Bernstein basis functions based algorithm for solving system of third order initial value problems
Alexandria Engineering Journal, 2021 For obtaining numerical solutions of the system of ordinary differential equations (ODEs) of third order, a new numerical technique is proposed by using operational matrices of Bernstein polynomials.
Rida Malik +6 more
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A polynomial interpolation process at quasi-Chebyshev nodes with the FFT [PDF]
Mathematics of Computation, 2011 Interpolation polynomial p n p_n at the
Hiroshi Sugiura, Takemitsu Hasegawa
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Hermite-Fejer interpolation at the ‘practical’ Chebyshev nodes [PDF]
Bulletin of the Australian Mathematical Society, 1973 Berman has raised the question in his work of whether Hermite-Fejér interpolation based on the so-called “practical” Chebyshev points, , 0(1)n, is uniformly convergent for all continuous functions on the interval [−1, 1]. In spite of similar negative results by Berman and Szegö, this paper shows this result is true, which is in accord with the great ...
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Electronic Journal of Qualitative Theory of Differential Equations, 2018 A constructive technique of analysis involving parametrisation and polynomial interpolation is suggested for general non-local problems for ordinary differential systems with locally Lipschitzian transcendental non-linearities.
András Rontó +2 more
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On Hermite-Fejér type interpolation on the Chebyshev nodes [PDF]
Bulletin of the Australian Mathematical Society, 1993 Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the ...
Byrne, Graeme J. +2 more
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Estimating the Lebesgue constant for the Chebyshev distribution of nodes
Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2023 In this paper an approach to estimation of the Lebesgue constant for the Lagrange interpolation process with nodes in the zeros of Chebyshev polynomials of the first kind is done. Two-sided estimation of this constant is carried out by using the logarithmic derivative of the Euler gamma function and of the Riemann zeta function.
Oksana V. Germider, Vasily N. Popov
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A generalization of Hermite interpolation
International Journal of Mathematics and Mathematical Sciences, 1997 We introduce a new interpolation at Chebyshev nodes.
Xie-Hua Sun, Tingfan Xie
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A collocation method to the solution of nonlinear fredholm-hammerstein integral and integro-differential equation [PDF]
Journal of Hyperstructures, 2013 This paper presents a computational technique for the solution of the nonlinear Fredholm-Hammerstein integral and integrodifferential equations. A hybrid of block-pulse functions and the second kind Chebyshev polynomials (hereafter called as HBC) is used
F. Mirzaee, Elham Hadadiyan
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Discrete orthogonal polynomials on Gauss–Lobatto Chebyshev nodes
Journal of Approximation Theory, 2007 This paper deals with explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev nodes \[ X_n=\{x_k=-\cos((k-1)\pi/(n-1))\},\quad k=1, 2, \ldots ,n. \] The orthogonal polynomials \(p_k(x)\) (\(k=1, 2, \dots ,n\)) with respect to the discrete inner product \(\langle f,g\rangle=\sum_{k=1}^nf(x_k)g(x_k)\) on the set \(
Eisinberg A, FEDELE, Giuseppe
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Abstract and Applied Analysis, 2012 Combining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre spectral method is applied to space discretization for numerically solving the Benjamin-Bona-Mahony-Burgers (gBBM-B) equations. The proposed approach is based on
Tinggang Zhao +5 more
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