Exponentially fitted multi-derivative linear methods for the resonant state of the Schrodinger equation

A new family of exponentially fitted P-stable one-step linear methods involving several derivatives for the numerical integration of the Schrodinger equation are obtained. Numerical results are reported to show the efficiency and robustness of the new methods specially adapted to the integration of the radial time-independent Schrodinger equation for large energies. Error analysis is carried out and the asymptotic expressions of the local errors for large energies explain the results of the numerical experiments on the resonance problem.