This article is cited in 14 papers

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

E. G. Khalilov

Azerbaijan State Oil and Industry University

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.

Key words: collocation method, mixed problem, Helmholtz equation, method of surface integral equations.

UDC: 519.633.6

Received: 18.03.2015
Revised: 07.10.2015

DOI: 10.7868/S0044466916070103

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:7, 1310–1318

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