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On the numerical treatment of an integral equation arising from a cruciform crack problem

✍ Scribed by G. Monegato; S. Prössdorf

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
575 KB
Volume
12
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider the following two integral equations
magnified image
the latter subject to the condition ∫v(y)d__y__ = 0, arising from the same problem of determining the distribution of stress in a thin elastic plate in the vicinity of a cruciform crack. In particular, we prove existence and uniqueness of the solutions of the two equations above in C[0, 1]. We also analyse the behaviour of ϕ(x) near the end‐point x = 0.

The therotical result obtained in the first part are then used in the last section to derive optimal rates of convergence for numerical methods, such as Galerkin, collocation and Nyström, applied to equation (1).

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