Abstract
A modification of the direct collocation and quadrature methods for the numerical solution of singular integral equations with Cauchy type kernels and index equal to 1 is proposed. This method is based on the replacement of the original singular integral equation by another one and the solution of the latter by the direct collocation, or quadrature, method. The advantage of the proposed algorithm is just that the condition supplementing the singular integral equation is no more separately considered and one more collocation point is used instead of it. The present algorithm is useful particularly for the solution of crack problems in the theory of plane or antiplane, static or dynamic elasticity. The equivalence of the proposed modification with the direct collocation and quadrature methods for solving the original singular integral equation is also proved and numerically verified.
Published Version
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