title: Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrödinger equation.
abstract: In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schrödinger equation. A particular scaling is used in the equation, which permits us 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, be equal for large distances. In order to obtain fast convergence, the secant method is used.
authors.affiliation: Instituto de Física Teórica, Universidade Estadual Paulista, 01405-900 São Paulo, Brazil.
authors.forename: A
authors.initials: A
authors.lastname: Gammal
authors.forename: T
authors.initials: T
authors.lastname: Frederico
authors.forename: L
authors.initials: L
authors.lastname: Tomio