Communications in Mathematical Sciences
Volume 13 (2015)
Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics
Pages: 1051 – 1074
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 the analytical breakdown of regularity of solutions to quasilinear Schrödinger equations. Numerical tests are performed for a modified version of the superfluid thin film equation.
Strang splitting, quasilinear Schrödinger equations, convergence, stability, blow-up
2010 Mathematics Subject Classification