Journal ArticleDOI
Numerical analysis : with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable
Zdeněk Kopal
- Vol. 125, Iss: 2, pp 288
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The article was published on 1962-01-01. It has received 33 citations till now. The article focuses on the topics: Numerical stability & Numerical analysis.read more
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Parallel methods for the numerical integration of ordinary differential equations
TL;DR: In this paper, a class of numerical integration formulas of a parallel type for ordinary differential equations is derived and conditions for the convergence of such formulas are formulated, and results of numerical experiments are given which show an effective improvement in computation speed.
Journal ArticleDOI
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.