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We study the Strang splitting scheme for quasilinear Schr\"odinger equations.We establish the convergence of the scheme for solutions with small initialdata. We analyze the linear instability of the numerical scheme, which explainsthe numerical blow-up of large data solutions and connects to analyticalbreakdown of regularity of solutions to quasilinear Schr\"odinger equations.Numerical tests are performed for a modified version of the superfluid thinfilm equation.

Strang Splitting Methods for a quasilinear Schr\"odinger equation - Convergence, Instability and Dynamics