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A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems. (English) Zbl 1196.65123
Summary: A dissipative exponentially-fitted method for the numerical integration of the Schrödinger equation and related problems is developed. The method is called dissipative since is a nonsymmetric multistep method. An application to the the resonance problem of the radial Schrödinger equation and to other well known related problems indicates that the new method is more efficient than the corresponding classical dissipative method and other well known methods. Based on the new method and the method of Raptis and Cash 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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
65L12Finite difference methods for ODE (numerical methods)