This paper deals with the numerical solution of a class of systems of Cauchy singular integral equations with constant coefficients. The proposed procedure consists of two basic steps: the first one is to consider a modified problem equivalent to the original one under suitable conditions, the second one is to approximate its solution by means of a vector of polynomial functions. Such array is constructed by applying a quadrature type method, based on Gaussian rules, that leads to solve a determined and well conditioned linear system. The convergence and stability of the method are proved in weighted L2 spaces. Some numerical tests are also shown.
Numerical solution of systems of Cauchy singular integral equations with constant coefficients
DE BONIS, Maria Carmela;LAURITA, Concetta
2012-01-01
Abstract
This paper deals with the numerical solution of a class of systems of Cauchy singular integral equations with constant coefficients. The proposed procedure consists of two basic steps: the first one is to consider a modified problem equivalent to the original one under suitable conditions, the second one is to approximate its solution by means of a vector of polynomial functions. Such array is constructed by applying a quadrature type method, based on Gaussian rules, that leads to solve a determined and well conditioned linear system. The convergence and stability of the method are proved in weighted L2 spaces. Some numerical tests are also shown.File | Dimensione | Formato | |
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