Dementjev, Aleksandr; Ivanauskas, Feliksas The convergence of splitting schemes for solving a system of nonlinear nonstationary Schrödinger type equations. (Russian. English summary) Zbl 0751.65060 Differ. Uravn. Primen. 46, 42-57 (1991). The authors prove the convergence of splitting schemes for a system of nonlinear nonstationary Schrödinger equations in discrete norms \(W^ 1_ 2\), \(C^ 1\). In three-dimensional space variables, the stability of the scheme is proved in the norm \(L_ 2\). There are no restrictions on the ratio of the time step to the spatial step. Reviewer: Qin Mengzhao (Beijing) MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) 35K55 Nonlinear parabolic equations Keywords:convergence; splitting schemes; system of nonlinear nonstationary Schrödinger equations; stability PDFBibTeX XMLCite \textit{A. Dementjev} and \textit{F. Ivanauskas}, Differ. Uravn. Primen. 46, 42--57 (1991; Zbl 0751.65060)