Título
Regularization of divergent integrals: A comparison of the classical and generalized-functions approaches
Autor
VOLODYMYR ZOZULYA
Nivel de Acceso
Acceso Abierto
Identificador alterno
doi: DOI: 10.1007/s10444-014-9399-3
Materias
Resumen o descripción
This article considers methods of weakly singular and hypersingular integral regularization based on the theory of distributions. For regularization of divergent integrals, the Gauss–Ostrogradskii theorem and the second Green’s theorem in the sense of the theory of distribution have been used. Equations that allow easy calculation of weakly singular, singular, and hypersingular integrals in one- and two-dimensional cases for any sufficiently smooth function have been obtained. These equations are compared with classical methods of regularization. The results of numerical calculation using classical approaches and those based of the theory of generalized functions, along with a comparison for different functions, are presented in tables and graphs of the values of divergent integrals versus the position of the colocation point.
Fecha de publicación
2015
Tipo de publicación
Artículo
Versión de la publicación
Versión publicada
Recurso de información
Formato
application/pdf
Fuente
Advances in Computational Mathematics, 41(4), 727-780, 2015
Idioma
Inglés
Sugerencia de citación
Zozulya, V. V. (2015). Regularization of divergent integrals: A comparison of the classical and generalized-functions approaches. Advances in Computational Mathematics, 41(4), 727-780.
Repositorio Orígen
Repositorio Institucional CICY
Descargas
1714