Convergence of the Galerkin methods for equations with elliptic operators on subspaces and solving the electric field equation

Application of the Galerkin methods to the numerical analysis of the integro-differential electric field equation is justified. The convergence of the Galerkin methods is established for a class of equations with nonelliptic operators comprising the electric field equation. Theorems concerning the approximation of the elements belonging to a special Sobolev space by the basis Rao–Wilton–Glisson functions are proved. The rate of convergence is estimated.