Modified Gauss-Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals | Zendy

P. S. Theocaris | Zendy

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Modified Gauss-Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals

Author(s) -

P. S. Theocaris

Publication year - 1983

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/s0161171283000526

Subject(s) - mathematics , cauchy principal value , singularity , numerical analysis , singular integral , numerical integration , convergence (economics) , mathematical analysis , initial value problem , iterated function , gauss , singular value , integral equation , boundary value problem , eigenvalues and eigenvectors , cauchy boundary condition , physics , quantum mechanics , economic growth , economics , free boundary problem

A numerical technique, first reported in 1979 in refs.[1] and [2], for the numerical evaluation of two-dimensional Cauchy-type principal-value integrals, isextended in this paper to include several cubature formlas of the Radau and Lobatto types. For the construction of such a cubature formula the 2-D singular integral is considered as an iterated one, and the second-order pole involved in this integral analyzed into a pair of complex poles. Based on this procedure, the methods of numerical integration, valid for one-dimensional singular integrals, are extanded to the case of two-dimensional singular integrals. The cubature formulas of the Lobatto- and Radau-type are now formulated to include the cases where some of the desired abscissas may be chosen accordins to any appropriate criterion

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