Dissipative exponentially-fitted methods for the numerical solution of the Schrödinger equation

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.