Strang Splitting Methods for a quasilinear Schrödinger equation - Convergence, Instability and Dynamics
For researchers in numerical analysis of PDEs, this work provides convergence guarantees and instability explanations for a class of quasilinear Schrödinger equations, though results are incremental for small data and instability analysis is specific to the scheme.
The paper proves convergence of Strang splitting for quasilinear Schrödinger equations with small initial data and identifies linear instability causing numerical blow-up for large data, linking to analytical regularity breakdown. Numerical tests on a modified superfluid thin film equation confirm the findings.
We study the Strang splitting scheme for quasilinear Schrödinger equations. We establish the convergence of the scheme for solutions with small initial data. We analyze the linear instability of the numerical scheme, which explains the numerical blow-up of large data solutions and connects to analytical breakdown of regularity of solutions to quasilinear Schrödinger equations. Numerical tests are performed for a modified version of the superfluid thin film equation.