A SEMI-DISCRETE LARGE-TIME BEHAVIOR PRESERVING SCHEME FOR THE AUGMENTED BURGERS EQUATION

被引：3
|
作者：
Ignat, Liviu I. [1 ]
Pozo, Alejandro [2 ,3 ]
机构：
[1] Romanian Acad, Inst Math Simion Stoilow, 21 Calea Grivitei St, Bucharest 010702, Romania
[2] Asociac Innovalia, Carretera Asua 6, Las Arenas Getxo 48930, Spain
[3] BCAM, Alameda Mazarredo 14, Bilbao 48009, Spain
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2017年 / 51卷 / 06期
基金：
欧洲研究理事会;
关键词：
Augmented Burgers equation; numerical approximation; large-time behavior; PROPAGATION; PREDICTION; WAVES; MODEL;
D O I：
10.1051/m2an/2017029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain L-1-L-p decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term K * u(xx) is the same as u(xx) for large times. Then, we propose a semi-discrete numerical scheme that preserves this asymptotic behavior, by introducing two correcting factors in the discretization of the non-local term. Numerical experiments illustrating the accuracy of the results of the paper are also presented.
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页码：2367 / 2398
页数：32
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