Unconditional \(L_\infty\) convergence of a compact ADI scheme for coupled nonlinear Schrödinger system
A three-level compact ADI scheme is developed to solve the two-dimensional coupled nonlinear Schrödinger (CNLS) system for which, using \(L_{\infty}\) estimates, it is proved that the new scheme is second-order accurate in time variable and fourth-order accurate in space variable, and stable. Numerical experiments demonstrate that the method is highly accurate and efficient. It can be directly extended to the three-dimensional CNLS system and multi-dimensional nonlinear Schödinger-type equations.
scientific article; zbMATH DE number 7188155
scientific article