The approximate solution of singular integro-differential equations systems on smooth contours in spaces \(L_p\) (Q1388076)

This article generalizes the results which were obtained by \textit{V. Zolatarevschi} and \textit{Iu. Caraus} [The approximate solution of singular integrodifferential equations on smooth contours in the spaces \(L_p\). Kishinev, Comput. Sci. J. Mold. 5, No. 1, 44-54 (1997; Zbl 0905.65129)]. A theoretical foundation of the collocation method and of the mechanical quadrature method for systems of singular integro-differential equations in the case when the equations are given on a closed contour satisfying some conditions of smoothness, without their reduction to the unit circle is given.