A Dissipative Exponentially-Fitted Method for the Numerical Solution of the Schrödinger Equation

A dissipative exponentially fitted method is constructed in this paper for the numerical integration of the Schrödinger equation. We note that the present method is a nonsymmetric multistep method (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 (i.e. more accurate and more rapid) than the classical dissipative method and other well-known methods. Based on the new method and the method of Raptis and Allison(19) 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 efficiency of the new approach.

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