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

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Abstract
We consider the following two integral equations magnified image the latter subject to the condition ∫v(y)dy = 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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