ON THE NUMERICAL-SOLUTION OF A LOGARITHMIC INTEGRAL-EQUATION OF THE 1ST KIND FOR THE HELMHOLTZ-EQUATION

Authors
KRESS R SLOAN IH
Citation
R. Kress et Ih. Sloan, ON THE NUMERICAL-SOLUTION OF A LOGARITHMIC INTEGRAL-EQUATION OF THE 1ST KIND FOR THE HELMHOLTZ-EQUATION, Numerische Mathematik, 66(2), 1993, pp. 199-214
Citations number
13
Categorie Soggetti
Mathematics,Mathematics
Journal title
Numerische Mathematik → ACNP
ISSN journal
0029599X
Volume
66
Issue
2
Year of publication
1993
Pages
199 - 214
Database
ISI
SICI code
0029-599X(1993)66:2<199:OTNOAL>2.0.ZU;2-8
Abstract
We describe a quadrature method for the numerical solution of the loga rithmic integral equation of the first kind arising from the single-la yer approach to the Dirichlet problem for the two-dimensional Helmholt z equation in smooth domains. We develop an error analysis in a Sobole v space setting and prove fast convergence rates for smooth boundary d ata.