Midpoint collocation for Cauchy singular integral equations

Chandler G.A. (1992) Midpoint collocation for Cauchy singular integral equations. Numerische Mathematik, 62 1: 483-509. doi:10.1007/BF01396240


Author Chandler G.A.
Title Midpoint collocation for Cauchy singular integral equations
Journal name Numerische Mathematik   Check publisher's open access policy
ISSN 0029-599X
Publication date 1992
Sub-type Article (original research)
DOI 10.1007/BF01396240
Volume 62
Issue 1
Start page 483
End page 509
Total pages 27
Publisher Springer-Verlag
Subject 2605 Computational Mathematics
2604 Applied Mathematics
2600 Mathematics
Abstract A Cauchy singular integral equation on a smooth closed curve may be solved numerically using continuous piecewise linear functions and collocation at the midpoints of the underlying grid. Even if the grid is non-uniform, suboptimal rates of convergence are proved using a discrete maximum principle for a modified form of the collocation equations. The same techniques prove negative norm estimates when midpoint collocation is used to determine piecewise constant approximations to the solution of first kind equations with the logarithmic potential.
Keyword Mathematics Subject Classification (1991): 65R20, 45L10
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: Scopus Import
 
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Created: Tue, 26 Jul 2016, 02:17:56 EST by System User