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Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation

A. Gammal·T. Frederico·L. Tomio
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Abstract

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used in the equation, which permits to evaluate the wave-function normalization after the numerical solution. We have a two point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, are equal for large distances. In order to obtain fast convergence, the secant method is used.

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A. Gammal, T. Frederico, L. Tomio. 1999-05-07. Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation. https://doi.org/10.1103/physreve.60.2421

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