A fast algorithm for the solution of the time-independent Gross–Pitaevskii equation

A new efficient numerical method for the solution of the time-independent Gross–Pitaevskii partial differential equation in three spatial variables is introduced. This equation is converted into an equivalent fixed-point form and is discretized using the collocation method at zeros of Legendre polynomials. Numerical comparisons with a state-of-the-art method based on propagating the solution of the time-dependent Gross–Pitaevskii equation in imaginary time are presented.