Abstract
In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of first order. We also analyze the large-time behavior of the approximated solution by obtaining the first term in the asymptotic expansion. We prove that, when time increases, these solutions behave as the self-similar solutions of the viscous Burgers equation.
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Acknowledgements
The authors thank the anonymous referees for the valuable comments that improved the first version of this paper. This work began during the visit of A.P. to IMAR and was finished during the visit of L.I. to BCAM. The authors thank these centers for the hospitality during their visits.
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Communicated by Christian Lubich.
L. I. Ignat was partially supported by Grant PN-II-RU-TE-2014-4-0007 of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, Grant MTM2014-52347, MICINN, Spain and FA9550-15-1-0027 of AFOSR. A. Pozo was granted by the Basque Government, reference PRE_2013_2_150, and partially supported by ERCEA under Grant 246775 NUMERIWAVES, by the Basque Government through the BERC 2014-2017 program and by Spanish MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323.
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Ignat, L.I., Pozo, A. A splitting method for the augmented Burgers equation. Bit Numer Math 58, 73–102 (2018). https://doi.org/10.1007/s10543-017-0673-x
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DOI: https://doi.org/10.1007/s10543-017-0673-x