Adaptive splitting methods for nonlinear Schrodinger equations in the semiclassical regime

被引：8

作者：

Auzinger, Winfried ^{[1
]}

Kassebacher, Thomas ^{[2
]}

Koch, Othmar ^{[3
]}

Thalhammer, Mechthild ^{[2
]}

机构：

[1] Vienna Univ Technol, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[2] Leopold Franzens Univ Innsbruck, Inst Math, Tech Str 13, A-6020 Innsbruck, Austria

[3] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

NUMERICAL ALGORITHMS | 2016年 / 72卷 / 01期

基金：

奥地利科学基金会;

关键词：

Nonlinear Schrodinger equations; Semiclassical regime; Splitting methods; Adaptive time integration; Local error; Convergence; COMPUTATIONAL METHODS; TIME; CONVERGENCE; STABILITY;

D O I：

10.1007/s11075-015-0032-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The error behavior of exponential operator splitting methods for nonlinear Schrodinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the dependence on the semiclassical parameter is identified. This is enabled within a defect-based framework which also suggests asymptotically correct a posteriori local error estimators as the basis for adaptive time stepsize selection. Numerical examples substantiate and complement the theoretical investigations.

引用

页码：1 / 35

页数：35

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