A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential (Analysis in Theory and Applications, 2017)
In the present paper a numerical method is developed to approximate thesolution of two-dimensional Nonlinear Schrödinger equation in the presence of a singular potential. The method leads to generalized Lyapunov-Sylvester algebraic operators that are shown to be invertible using original topological and differential calculusissued methods. The numerical scheme is proved to be consistent, convergent and stable using the Lyapunov criterion, lax equivalence theorem and the properties of thegeneralized Lyapunov-Sylvester operators.
Keywords: NLS equation; finite-difference scheme; stability analysis; Lyapunov criterion; consistency; convergence; error estimates; Lyapunov operator.