Exponentially- fitted St�rmer-Verlet methods

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 St�rmer/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 Schr�dinger 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.


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