Numerical solutions of Cauchy singular integral equations using generalized inverses

S. Kim

doi:10.1016/S0898-1221(99)00225-4

Numerical solutions of Cauchy singular integral equations using generalized inverses

S. Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Solving singular integral equations of Cauchy-type numerically involves solution of a linear system of equations. The number of collocation and quadrature points decides the size of the linear system and an n×n matrix is derived in most cases. Taking more collocation points may yield more accurate numerical solutions as in [1] and numerical difficulties arising in solving overdetermined system. We show that the coefficient matrix of the overdetermined system obtained by taking more collocation points than quadrature nodes have the generalized inverse.

Original language	English
Pages (from-to)	183-195
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	38
Issue number	5
DOIs	https://doi.org/10.1016/S0898-1221(99)00225-4
State	Published - Sep 1999

Bibliographical note

Funding Information:
Research supported by Korean Ministry of Education, BSKI-98-1430 and KOSEF 97-0701-01-01-3. The author wishes to thank R. P. Srivastav for his helpful comments and R. P. Tewarson for his hospitality during the author's visit to SUNY Stony Brook where the final version of the present paper was written.

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title = "Numerical solutions of Cauchy singular integral equations using generalized inverses",

abstract = "Solving singular integral equations of Cauchy-type numerically involves solution of a linear system of equations. The number of collocation and quadrature points decides the size of the linear system and an n×n matrix is derived in most cases. Taking more collocation points may yield more accurate numerical solutions as in [1] and numerical difficulties arising in solving overdetermined system. We show that the coefficient matrix of the overdetermined system obtained by taking more collocation points than quadrature nodes have the generalized inverse.",

author = "S. Kim",

note = "Funding Information: Research supported by Korean Ministry of Education, BSKI-98-1430 and KOSEF 97-0701-01-01-3. The author wishes to thank R. P. Srivastav for his helpful comments and R. P. Tewarson for his hospitality during the author's visit to SUNY Stony Brook where the final version of the present paper was written.",

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N2 - Solving singular integral equations of Cauchy-type numerically involves solution of a linear system of equations. The number of collocation and quadrature points decides the size of the linear system and an n×n matrix is derived in most cases. Taking more collocation points may yield more accurate numerical solutions as in [1] and numerical difficulties arising in solving overdetermined system. We show that the coefficient matrix of the overdetermined system obtained by taking more collocation points than quadrature nodes have the generalized inverse.

AB - Solving singular integral equations of Cauchy-type numerically involves solution of a linear system of equations. The number of collocation and quadrature points decides the size of the linear system and an n×n matrix is derived in most cases. Taking more collocation points may yield more accurate numerical solutions as in [1] and numerical difficulties arising in solving overdetermined system. We show that the coefficient matrix of the overdetermined system obtained by taking more collocation points than quadrature nodes have the generalized inverse.

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 5

ER -

Numerical solutions of Cauchy singular integral equations using generalized inverses

Abstract

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