Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrodinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schrodinger equation. A particular scaling is used in the equation, which permits us to evaluate the wavefunction 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, be equal for large distances. In order to obtain fast convergence, the secant method is used. [S1063-651X(99)04608-5].