Skip to main content

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

Publication ,  Journal Article
Lu, J; Marzuola, JL
Published in: Communications in Mathematical Sciences
January 1, 2015

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.

Duke Scholars

Published In

Communications in Mathematical Sciences

DOI

EISSN

1945-0796

ISSN

1539-6746

Publication Date

January 1, 2015

Volume

13

Issue

5

Start / End Page

1051 / 1074

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Lu, J., & Marzuola, J. L. (2015). Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics. Communications in Mathematical Sciences, 13(5), 1051–1074. https://doi.org/10.4310/CMS.2015.v13.n5.a1
Lu, J., and J. L. Marzuola. “Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics.” Communications in Mathematical Sciences 13, no. 5 (January 1, 2015): 1051–74. https://doi.org/10.4310/CMS.2015.v13.n5.a1.
Lu J, Marzuola JL. Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics. Communications in Mathematical Sciences. 2015 Jan 1;13(5):1051–74.
Lu, J., and J. L. Marzuola. “Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics.” Communications in Mathematical Sciences, vol. 13, no. 5, Jan. 2015, pp. 1051–74. Scopus, doi:10.4310/CMS.2015.v13.n5.a1.
Lu J, Marzuola JL. Strang splitting methods for a quasilinear Schrödinger equation: Convergence, instability, and dynamics. Communications in Mathematical Sciences. 2015 Jan 1;13(5):1051–1074.

Published In

Communications in Mathematical Sciences

DOI

EISSN

1945-0796

ISSN

1539-6746

Publication Date

January 1, 2015

Volume

13

Issue

5

Start / End Page

1051 / 1074

Related Subject Headings

  • Applied Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 1502 Banking, Finance and Investment
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics