title: Dissipative exponentially-fitted methods for the numerical solution of the Schrödinger equation.
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.
authors.affiliation: School of Engineering, Department of Civil Engineering, Democritus University of Thrace, Xanthi, Greece. tsimos@mail.ariadne-t.gr
authors.forename: T E
authors.initials: TE
authors.lastname: Simos
authors.forename: P S
authors.initials: PS
authors.lastname: Williams