Summary
In the papers [1] - [4] the quadrature-differences methods for the various classes of the 1-dimensional periodic singular integro-differential equations with Hilbert kernels were justified. The convergence of the methods was proved and error estimates were obtained. Here we propose and justify the cubature-differences method for 2-dimensional 1 linear periodic singular integro-differential equations. Such equations appear in the theory of elastity (see [5]) and in some problems of diffraction of electromagnetic waves (see e.g. [6]) The convergence of the method is proved and error estimate is obtained.
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References
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Fedotov, A.I. (2004). Cubature-Differences Method for Singular Integro-differential Equations. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_28
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DOI: https://doi.org/10.1007/978-3-642-18775-9_28
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