Abstract:
A justification for the collocation method for a system of integral equations of magnetic boundary value problems for the Helmholtz vector equation is given. At certain selected points, the system of integral equations is replaced by a system of algebraic equations, and the existence and uniqueness of a solution to the system of algebraic equations is established. Convergence of the solution of the system of algebraic equations to the exact solution of the system of integral equations is proved, and the rate of convergence of the method is indicated. Furthermore, a sequence converging to the exact solution of magnetic boundary value problems is constructed.
Key words:magnetic boundary value problems, vector potentials, Helmholtz vector equation, systems of integral equations.
