A family of \(P\)-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation (Q1976652)

This paper deals with a new approach for constructing exponentially-fitted methods. Using this approach the author constructs methods which exactly integrate functions and which are \(P\)-stable. Two \(P\)-stable exponentially-fitted methods are obtained. The new methods are applied to the resonance problem (which arises from the one-dimensional Schrödinger equation) with two different types of potentials.