Multigrid and adaptive algorithm for solving the nonlinear Schrödinger equation (Q920613)

An application of a multigrid and adaptive algorithm for solving the initial-boundary value problem \(iu_ t-(\partial /\partial x)A(x)(\partial u/\partial x)+2| u|^ 2u+F(x,t)u=G(x,t),\quad u\in {\mathbb{R}}^ m,\) \(x_ L<x<x_ R,\quad u|_{x_ L}=u|_{x_ R}=0,\quad u|_{t=0}=u_ 0(x),\) where A(x) is a real diagonal matrix, is considered. There are estimates for the solution of the difference scheme. Some numerical examples are presented and compared with corresponding results obtained by a traditional method. There is a discussion of the method and the numerical results.