Geodesic
On convergence of quadrature-differences method for linear singular integro-differential equations on the interval
Archivum mathematicum, Tome 37 (2001) no. 4, pp. 257-271.

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Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval $(-1,1)$. We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation.
Classification : 45E05, 45L05, 65R20
Keywords: singular integro-differential equations; quadrature-differences method 
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     author = {Fedotov, A. I.},
     title = {On convergence of quadrature-differences method for linear singular integro-differential equations on the interval},
     journal = {Archivum mathematicum},
     pages = {257--271},
     publisher = {mathdoc},
     volume = {37},
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     year = {2001},
     mrnumber = {1879448},
     zbl = {1090.45003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2001__37_4_a1/}
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Fedotov, A. I. On convergence of quadrature-differences method for linear singular integro-differential equations on the interval. Archivum mathematicum, Tome 37 (2001) no. 4, pp. 257-271. http://geodesic.mathdoc.fr/item/ARM_2001__37_4_a1/