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The Numerical Solution of Boundary Integral Kendall E. Atkinson

Summary: The Numerical Solution of Boundary Integral
Kendall E. Atkinson
Dept. of Mathematics, The University of Iowa
Much of the research on the numerical analysis of Fredholm type in-
tegral equations during the past ten years has centered on the solution of
boundary integral equations (BIE). A great deal of this research has been
on the numerical solution of BIE on simple closed boundary curves S for
planar regions. When a BIE is de ned on a smooth curve S, there are
many numerical methods for solving the equation. The numerical analysis
of most such problems is now well-understood, for both BIE of the rst
and second kind, with many people having contributed to the area. For
the case with the BIE de ned on a curve S which is only piecewise smooth,
new numerical methods have been developed during the past decade. Such
methods for BIE of the second kind were developed in the mid to late 80s
and more recently, high order collocation methods have been given and an-
alyzed for BIE of the rst kind. The numerical analysis of BIE on surfaces
S in R3


Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa
Marzano, Frank Silvio - Dipartimento di Ingegneria Elettronica, UniversitÓ di Roma "La Sapienza"


Collections: Computer Technologies and Information Sciences; Engineering; Geosciences