A note on the numerical solution of the semilinear Schrödinger equation Original Research Article

The unique solvability of local and nonlocal boundary value problems for the semilinear Schrödinger equation in a Hilbert space is investigated. The convergence estimates for the solution of difference schemes are established. Some numerical examples illustrating the methods described in our work are given. Applicability of these methods to nonlinear Schrödinger equation is discussed.