Solution of a Schroedinger equation by iterative refinement

A simple eigenvalue and a corresponding wavefunction of a Schroedinger operator is initially approximated by the Galerkin method and by the iterated Galerkin method of Sloan. The initial approximation is iteratively refined by employing three schemes: the Rayleigh-Schroedinger scheme, the fixed point scheme and a modification of the fixed point scheme. Under suitable conditions, convergence of these schemes is established by considering error bounds. Numerical results indicate that the modified fixed point scheme along with Sloan's method performs better than the others. 7 refs., 4 tabs., 4 figs