Regular approximation of singular self-adjoint differential operators

Given a singular self-adjoint differential operator L̂ of order 2n with real coefficients we construct two sequences of regular self-adjoint differential expressions L̂^r which converge to L̂ in a generalized sense of resolvent convergence. The first construction is suitable when no information about the real resolvent set of L̂ is available. The second is suitable when we know a real point of the resolvent set of L̂. The main application of this construction is in numerical solution of singular differential equations.