A Lawson-type exponential integrator for the Korteweg-de Vries equation

被引：20
作者：
Ostermann, Alexander [1 ]
Su, Chunmei [1 ]
机构：
[1] Univ Innsbruck, A-6020 Innsbruck, Austria
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2020年 / 40卷 / 04期
关键词：
exponential integrators; Lawson methods; Korteweg-de Vries equation; error estimates; Rusanov scheme; FOURIER PSEUDOSPECTRAL METHOD; LEGENDRE-PETROV-GALERKIN; FINITE-ELEMENT METHOD; KADOMTSEV-PETVIASHVILI; DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; OPERATOR; KDV; CONVERGENCE; STABILITY;
D O I：
10.1093/imanum/drz030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose an explicit numerical method for the periodic Korteweg-de Vries equation. Our method is based on a Lawson-type exponential integrator for time integration and the Rusanov scheme for Burgers' nonlinearity. We prove first-order convergence in both space and time under a mild Courant-FriedrichsLewy condition tau = O(h), where tau and h represent the time step and mesh size for solutions in the Sobolev space H-3((-pi, pi)), respectively. Numerical examples illustrating our convergence result are given.
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页码：2399 / 2414
页数：16
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