A New Concept in Near-Singular Integral Evaluation: The Continuation Approach
The functional homogeneity of Green functions is exploited in the derivation of continuation formulae for the accurate evaluation of near singular integrals. These formulae provide a means of systematically continuing such unconventional integrals as the principal value and finite part integrals of...
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| Veröffentlicht in: | SIAM journal on applied mathematics 1989-10, Vol.49 (5), p.1285-1295 |
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| container_end_page | 1295 |
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| container_issue | 5 |
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| container_title | SIAM journal on applied mathematics |
| container_volume | 49 |
| creator | Vijayakumar, Sinnathurai Cormack, Donald E. |
| description | The functional homogeneity of Green functions is exploited in the derivation of continuation formulae for the accurate evaluation of near singular integrals. These formulae provide a means of systematically continuing such unconventional integrals as the principal value and finite part integrals of singular functions to conventional integrals of nonsingular functions. A new concept, the notion of continuum integral, which is applicable to singular as well as to nonsingular integrals, is introduced as a generalization of principal value and finite part integrals. Numerical examples are provided that illustrate the computational advantages of the continuation method and give a new perspective on the subtleties of singular and near-singular integrals. |
| doi_str_mv | 10.1137/0149078 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0036-1399 |
| ispartof | SIAM journal on applied mathematics, 1989-10, Vol.49 (5), p.1285-1295 |
| issn | 0036-1399 1095-712X |
| language | eng |
| recordid | cdi_proquest_journals_916926009 |
| source | Jstor Complete Legacy; LOCUS - SIAM's Online Journal Archive; JSTOR Mathematics & Statistics |
| subjects | Boundary element method Cauchy mean value theorem Embeddings Exact sciences and technology Gaussian quadratures Integrals Integrands Mathematical functions Mathematical integrals Mathematical methods in physics Mathematical tables Numerical approximation and analysis Numerical quadratures Partial differential equations Physics Region of integration |
| title | A New Concept in Near-Singular Integral Evaluation: The Continuation Approach |
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