Geodesic
Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1340-1348

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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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     author = {E. G. Khalilov},
     title = {Justification of the collocation method for the integral equation for a mixed boundary value problem for the {Helmholtz} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1340--1348},
     publisher = {mathdoc},
     volume = {56},
     number = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a9/}
}
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E. G. Khalilov. Justification of the collocation method for the integral equation for a mixed boundary value problem for the Helmholtz equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1340-1348. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a9/