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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Journal ArticleDOI
Symmetric integration rules for hypercubes. II. Rule projection and rule extension
TL;DR: In this article, a theory is described which facilitates the construction of high-dimensional integration rules and it is shown that, for large n, an n-dimensional integrated rule of degree 2t + 1 man can be constructed requiring a number of function evaluations of order 2'n ¡t
Journal ArticleDOI
Eberlein measure and mechanical quadrature formulae. I. Basic theory.
TL;DR: In this article, a theory of mechanical quadrature for k-fold integrals (k _ 1) is presented, and a rational basis for the global comparison of different quadratures methods is provided.
Journal ArticleDOI
Paper: Parallel algorithms for solving initial value problems: front broadening and embedded parallelism
D. Hutchinson,B. M. S. Khalaf +1 more
TL;DR: i) broadening of the computation front (BCF) techniques, and ii) block implicit (BI) methods to speed up the numerical solution of IVPS in ODEs by using MIMD computing systems are developed.
Journal ArticleDOI
Application Local Polynomial and Non-polynomial Splines of the Third Order of Approximation for the Construction of the Numerical Solution of the Volterra Integral Equation of the Second Kind
TL;DR: In this paper, the application of polynomial and non-polynomial splines to the solution of nonlinear Volterra integral equations is discussed. And the results of the numerical experiments are presented.
Journal ArticleDOI
Application of Splines of the Second Order Approximation to Volterra Integral Equations of the Second Kind. Applications in Systems Theory and Dynamical Systems
I. G. Burova,G. O. Alcybeev +1 more
TL;DR: In this article, the authors discussed the application of local interpolation splines of the second order of approximation for the numerical solution of Volterra integral equations of the first kind, and constructed a computational scheme based on the use of polynomial and non-polynomial splines.
References
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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.
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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.
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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.
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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.