Journal ArticleDOI
Numerical Analysis. With Emphasis on the Application of Numerical Techniques to Problems of Infinitesimal Calculus in Single Variable. By Z. Kopal. Pp. xiv, 556. 63s. 1955. (Chapman & Hall, London)
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This article is published in The Mathematical Gazette.The article was published on 1957-10-01. It has received 22 citations till now.read more
Citations
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Runge-Kutta methods with minimum error bounds
TL;DR: It is the purpose of this paper to derive Runge-Kutta methods of second, third and fourth order which have minimum truncation error bounds of a specified type.
Dissertation
Numerical approximation of highly oscillatory integrals
TL;DR: Olver et al. as discussed by the authors investigated efficient methods for numerical integration of highly oscillatory functions, over both univariate and multivariate domains, and demonstrated that high oscillation is in fact beneficial: the methods discussed in this paper improve with accuracy as the frequency of oscillation increases.
Journal ArticleDOI
Numerical Integration over the n-Dimensional Spherical Shell
TL;DR: The n-dimensional generalisation of a theorem by W. H. Peirce as discussed by the authors provides a method for constructing product type integration rules of arbitrarily high polynomial precision over a hyperspherical shell region and using a weight function r. Table I lists orthogonal polynomials, coordinates and coefficients for integration points in the angular rules for 3rd and 7th degree precision.
Journal ArticleDOI
An algorithm for summing orthogonal polynomial series and their derivatives with applications to curve-fitting and interpolation
TL;DR: In this paper, an algorithm for summing orthogonal polynomial series and derivatives with applications to curve fitting and interpolation is presented. But this algorithm is not suitable for curve fitting.
Journal ArticleDOI
The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula. I. Functions whose early derivatives are continuous
TL;DR: In this paper, the M6bius inversion technique is applied to the Poisson summation formula, which results in expressions for the remainder term in the Fourier coefficient asymptotic expansion as an infinite series.
References
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Abscissas and weights for Lobatto quadrature of high order
TL;DR: In this article, the authors consider the case when the integrand vanishes at the two end points as it does in Longman's method for evaluating integrals of oscillating functions, and they consider the closed symmetric n-point integration rule with n odd, n = 2m + 1.
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Hybrid sixth order spatial discretization scheme for non-uniform Cartesian grids
TL;DR: In this article, a class of high accuracy compact schemes used to solve wave problems and the Navier Stokes equation (NSE) on a non-uniform Cartesian grid is presented.
Journal ArticleDOI
Thin conical shells with constant thickness and under axisymmetric load
TL;DR: In this paper, the Green's function for the homogeneous differential equation based on the bending theory was used to determine the stresses, strains and displacements of a truncated or complete thin conical shell with constant thickness and axisymmetric load distributed or concentrated along the meridian.
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An iterative method for the solution of eigenvalue problems
TL;DR: Several methods have been proposed to determine the proper elements (i.e. eigenvalues and eigenfunctions) of Sturm-Liouville equations as discussed by the authors, and most of them have been reviewed by Kopal [1], but we shall examine one of them, the so called Rayleigh-Ritz method, in order to explain the main defect they have in common and to judge their general efficiency.
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Quadrature Formulas for Infinite Integrals
TL;DR: In this paper, the Hermite-Gauss and LaguerreGauss quadratures for statistical integrands were compared with a weight function w(x) = (1 + x2) -k- for the range b = -a = cc.