Newton-Based Methods for Finding the Positive Ground State of Gross-Pitaevskii Equations

The discretization of Gross-Pitaevskii equations (GPE) leads to a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). We use two Newton-based methods compute the positive ground state GPE. first method comes from Newton-Noda iteration for saturable Schrödinger proposed by Ching-Sung Liu, which can be transferred GPE naturally. second combines idea root-finding and Newton method, in which, each subproblem involving block tridiagonal linear systems solved easily. give an explicit convergence computational complexity analysis it. Numerical experiments are provided support theoretical results.