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Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation

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Abstract

The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined.

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Authors and Affiliations

  1. Azerbaijan State Oil and Industry University, pr. Azaldyg 20, Baku, AZ 1010, Azerbaijan

    E. H. Khalilov

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  1. E. H. Khalilov
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Correspondence to E. H. Khalilov.

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Original Russian Text © E.H. Khalilov, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 7, pp. 1340–1348.

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Khalilov, E.H. Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation. Comput. Math. and Math. Phys. 56, 1310–1318 (2016). https://doi.org/10.1134/S0965542516070101

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  • DOI: https://doi.org/10.1134/S0965542516070101

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