Product integrationcollocation methods for noncompact integral operator equations
Authors:
G. A. Chandler and I. G. Graham
Journal:
Math. Comp. 50 (1988), 125138
MSC:
Primary 65R20
DOI:
https://doi.org/10.1090/S00255718198809178211
MathSciNet review:
917821
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Abstract  References  Similar Articles  Additional Information
Abstract: We discuss the numerical solution of a class of secondkind integral equations in which the integral operator is not compact. Such equations arise, for example, when boundary integral methods are applied to potential problems in a twodimensional domain with corners in the boundary. We are able to prove the optimal orders of convergence for the usual collocation and product integration methods on graded meshes, provided some simple modifications are made to the underlying basis functions. These are sufficient to ensure stability, but do not damage the rate of convergence. Numerical experiments show that such modifications are necessary in certain circumstances.

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Additional Information
Keywords:
Secondkind integral equations,
product integration,
boundary integral equations,
collocation
Article copyright:
© Copyright 1988
American Mathematical Society