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Dissipative exponentially-fitted methods for the numerical solution of the Schrödinger equation
1School of Engineering, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece. tsimos@mail.ariadne-t.gr
Abstract:
The first dissipative exponentially fitted method for the numerical integration of the Schrödinger equation is developed in this paper. The technique presented is a nonsymmetric multistep (dissipative) method. An application to the bound-states problem and the resonance problem of the radial Schrödinger equation indicates that the new method is more efficient than the classical dissipative method and other well-known methods. Based on the new method and the method of Raptis and Allison (Comput. Phys. Commun. 14 (1978) 1-5) a new variable-step method is obtained. The application of the new variable-step method to the coupled differential equations arising from the Schrödinger equation indicates the power of the new approach.