Fractional error estimates of splitting schemes for the nonlinear Schrodinger equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:442

Article

Eilinghoff, Johannes¹  Schnaubelt, Roland¹  Schratz, Katharina¹ 

[1] Karlsruhe Inst Technol, Dept Math, D-76128 Karlsruhe, Germany

关键词: Nonlinear Schrodinger equation;    Splitting;    Error analysis;    Stability;    Fractional convergence order;    Interpolation;   

DOI  :  10.1016/j.jmaa.2016.05.014

来源: Elsevier

【 摘 要 】

We investigate the Lie and the Strang splitting for the cubic nonlinear Schrodinger equation on the full space and on the torus in up to three spatial dimensions. We prove that the Strang splitting converges in L-2 with order 1+theta for initial values in H2+2 theta with theta is an element of (0,1) and that the Lie splitting converges with order one for initial values in H-2. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free