OPERATOR SPLITTING FOR PARTIAL DIFFERENTIAL EQUATIONS WITH BURGERS NONLINEARITY

被引：0

作者：

Holden, Helge ^{[1
,2
]}

Lubich, Christian ^{[3
]}

Risebro, Nils Henrik ^{[2
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Univ Oslo, Ctr Math Applicat, NO-0316 Oslo, Norway

[3] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany

来源：

MATHEMATICS OF COMPUTATION | 2013年 / 82卷 / 281期

关键词：

Operator splitting; Burgers equation; KdV equation; Benney-Lin equation; Kawahara equation; WAVES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a new analytical approach to operator splitting for equations of the type u(t) = A(u) + uu(x) where A is a linear differential operator such that the equation is well-posed. Particular examples include the viscous Burgers equation, the Korteweg-de Vries (KdV) equation, the Benney-Lin equation, and the Kawahara equation. We show that the Strang splitting method converges with the expected rate if the initial data are sufficiently regular. In particular, for the KdV equation we obtain second-order convergence in H-r for initial data in Hr+ 5 with arbitrary r >= 1.

引用

页码：173 / 185

页数：13

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