Abstract
We develop a numerical method based on parametric adaptive quintic spline functions for solving the nonlinear Schrödinger (NLS) equation. The truncation error is theoretically analyzed. Based on the von Neumann method and the linearization technique, stability analysis of the method is studied and the method is shown to be unconditionally stable. Two invariants of motion related to mass and momentum are calculated to determine the conservation properties of the problem. Finally, some numerical tests are presented to illustrate the method’s efficiency.
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