Volume 51, Number 6, November-December 2017
|Page(s)||2367 - 2398|
|Published online||18 December 2017|
A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation
1 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania.
2 Asociación Innovalia, Carretera de Asua 6, 48930 Las Arenas - Getxo, Spain.
3 BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain.
Received: 10 September 2014
Revised: 30 March 2017
Accepted: 1 June 2017
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 L1-Lp decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term K ∗ uxx is the same as uxx 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.
Mathematics Subject Classification: 35B40 / 65M12 / 35Q35
Key words: Augmented Burgers equation / numerical approximation / large-time behavior
© EDP Sciences, SMAI 2017
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