New formulae for higher order derivatives and applications

DOI10.1016/j.cam.2009.07.038zbMath1183.65024OpenAlexW1973670074MaRDI QIDQ732148

Hassan Safouhi, Richard Mikael Slevinsky

Publication date: 9 October 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.07.038

zbMATH Keywords

numerical integrationdifferential equationsspecial functionsBessel functionsHermite functionhigher order derivativesLegendre function

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Numerical differentiation (65D25) Numerical approximation and evaluation of special functions (33F05)

Related Items (9)

A recursive algorithm for the \(G\) transformation and accurate computation of incomplete Bessel functions ⋮ Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation ⋮ A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions ⋮ Greater Arrow-Pratt (absolute) risk aversion of higher orders ⋮ To study the hyperbolic annular fin with temperature dependent thermal conductivity via optimized Chebyshev polynomials with interior point algorithm ⋮ Hybrid polynomial approximation to higher derivatives of rational curves ⋮ Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation by a novel intelligent computational approach using optimized Chebyshev polynomials ⋮ Bessel, sine and cosine functions and extrapolation methods for computing molecular multi-center integrals ⋮ On the first positive and negative excursion exceeding a given length

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical treatment of a twisted tail using extrapolation methods
• Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
• Efficient and rapid numerical evaluation of the two-electron, four-center Coulomb integrals using nonlinear transformations and useful properties of sine and Bessel functions
• The Fourier transform method and the \(S\overline D\) approach for the analytical and numerical treatment of multicenter overlap-like quantum similarity integrals
• The properties of sine, spherical Bessel and reduced Bessel functions for improving convergence of semi-infinite very oscillatory integrals: the evaluation of three-centre nuclear attraction integrals overBfunctions
• An extremely efficient approach for accurate and rapid evaluation of three-centre two-electron Coulomb and hybrid integrals overBfunctions
• Extrapolation Methods for Oscillatory Infinite Integrals
• A New Method for Approximating Improper Integrals
• The Curious History of Faa di Bruno's Formula
• An extremely efficient and rapid algorithm for numerical evaluation of three-centre nuclear attraction integrals over Slater-type functions
• A new algorithm for accurate and fast numerical evaluation of hybrid and three-centre two-electron Coulomb integrals over Slater-type functions
• The SIAM 100-Digit Challenge
• The Integration of Bessel Functions

This page was built for publication: New formulae for higher order derivatives and applications