Date of Online Publication: 22/12/2006 Keywords: Exponetial fitting, Stormer/Verlet, oscillating problems, Schrodinger equations Authors: G. Vanden Berghe and M. Van Daele Pages: 241-255
Exponentially- fitted Störmer/Verlet methods are constructed taking into account a six-step flow chart. It is shown that the thus constructed methods, when applied to strongly oscillating problems, are equivalent respectively to Gautschi and Deulfhard methods. As an illustration the constructed algorithms are used to solve bounded states as well as resonance states of Schrödinger equations. It is seen that all the versions are of order four but the way the error on the eigenvalues increases with the energy differs from one version to the other for the two problems considered.