On Approximate Solutions of Magnetic Field Boundary Value Problems by the Method of a System of Integral Equations

A substantiation of the collocation method for a system of integral equations of magnetic field boundary value problems for the vector Helmholtz equation is presented. At certain selected points, the system of integral equations is replaced by a system of algebraic equations. The existence and uniqueness of a solution to this system is proved. Convergence of the solution to the system of algebraic equations to the exact solution of the system of integral equations is proved, and the convergence rate of the method is obtained. Furthermore, a sequence converging to the exact solution of the magnetic boundary value problems is constructed.