Journal ArticleDOI
Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity
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TLDR
An approach based on extrapolation is described that leads to a method not unlike the Romberg integration, and a set of useful expansions are stated.About:
This article is published in Journal of Computational Physics.The article was published on 1976-03-01. It has received 42 citations till now. The article focuses on the topics: Romberg's method & Extrapolation.read more
Citations
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Generalized neville type extrapolation schemes
TL;DR: In this paper, the generalized Neville extrapolation is generalized to expansions for which the extrapolation coefficients, used in the calculation of the elements in the related extrapolation table, are not known.
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Numerical solution of an exterior Neumann problem using a double layer potential
J. Giroire,Jean-Claude Nédélec +1 more
TL;DR: In this paper, the authors propose a variational formulation of the Dirichlet problem using a double layer potential, which is similar to the one we use in this paper, and obtain the existence and unicity of a solution and error estimates.
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Generalized Duffy transformation for integrating vertex singularities
S. E. Mousavi,N. Sukumar +1 more
TL;DR: In this paper, the authors generalize the Duffy trans-formation to power singularities of the form p(x)/r α, where p is a trivariate polynomial and α> 0 is the strength of the singularity.
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Numerical calculation of weakly singular surface integrals
TL;DR: In this paper, the authors consider semi-analytical and purely numerical integration methods for weakly singular integrals with point singularities on curved smooth surfaces and compare them as regards accuracy and computational efficiency.
Journal ArticleDOI
Computation of loop integrals using extrapolation
TL;DR: In this paper, a class of methods for the evaluation of loop integrals based on extrapolation is presented, based on generating a sequence of approximations which converge to the loop integral value as a parameter e introduced in the integrand tends to zero.
References
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Journal ArticleDOI
Numerical quadrature and asymptotic expansions
J. N. Lyness,Barry W. Ninham +1 more
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An error functional expansion for $N$-dimensional quadrature with an integrand function singular at a point
TL;DR: In this article, the error function expansion for the error functional with integrand function F(x) = ln rf(x), the only singularity being at the origin, a vertex of the unit hypercube of integration is derived.