Communications in Mathematical Sciences

Volume 13 (2015)

Number 5

Strang splitting methods for a quasilinear Schrödinger equation: convergence, instability, and dynamics

Pages: 1051 – 1074

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n5.a1

Authors

Jianfeng Lu (Departments of Mathematics, Physics, and Chemistry, Duke University, Durham, North Carolina, U.S.A.)

Jeremy L. Marzuola (Department of Mathematics, University of North Carolina, Chapel Hill, U.S.A.)

Abstract

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.

Keywords

Strang splitting, quasilinear Schrödinger equations, convergence, stability, blow-up

2010 Mathematics Subject Classification

35Q55, 65M70

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