Abstract:
The paper presents a substantiation of the collocation method for a system of integral equations for the field-matching boundary value problem for the Helmholtz equation in two-dimensional space. Quadrature formulas are constructed for the single and double layer potentials and the normal derivative of the single layer potential. At definite points, the system of integral equations is replaced by a system of algebraic equations, and the existence and uniqueness of a solution of the system of algebraic equations is shown. The convergence of the solution of a system of algebraic equations to the exact solution of a system of integral equations is proved, and the convergence rate of the method is found. In addition, a sequence is constructed that converges to the exact solution of the field-matching boundary value problem.
Key words:field-matching boundary value problem, Helmholtz equation, system of integral equations, single and double layer potentials, Hankel function
quadrature formulas, collocation method.
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