A Numerical Approach for (2+1)D Saturable Nonlinear Schrödinger Equations With Generalized Loss

ABSTRACT

This paper details a standard Crank‐Nicolson finite difference (CNFD) discretization for the ()D nonlinear Schrödinger equation with saturable nonlinearity and a generalized loss. This study establishes the fundamental properties of the numerical scheme, including the boundedness, existence, and uniqueness of its discrete solution. A generalized approach is introduced to derive error estimates, specifically for the boundedness of the discrete norm. These estimates are subsequently employed to rigorously prove the optimal second‐order convergence of the numerical solution in both the discrete and norms. The theoretical claims are verified through a series of illustrative numerical experiments.