Finite elements for the eigenvalue problem of differential operators in unbounded intervals

The eigenvalue problem for one‐dimensional differential operators with a possible essential spectrum is discretized with finite elements defined on a bounded interval together with a fundamental system of the differential equation outside of the interval. A non‐pollution property of the discrete spectra is proved and the error in the approximation of isolated eigenvalues and corresponding eigenvectors is estimated. The convergence of some numerical algorithms for the solution of the subsequent discrete nonlinear eigenvalue problem is proved. The method is tested in some numerical examples.