×
Tsai, Chih-Ching; Shih, Yin-Tzer; Lin, Yu-Tuan; Wang, Hui-Ching

Tailored finite point method for solving one-dimensional Burgers’ equation. (English) Zbl 1364.65219

Int. J. Comput. Math. 94, No. 4, 800-812 (2017).
Summary: We propose a tailored finite point method (TFPM) for solving a quasilinear time-dependent Burgers’ equation with a small coefficient of viscosity. The selected basis functions for the TFPM automatically fit the properties of the local solution in time and space simultaneously. The stability and error analysis for the TFPM are given. We also demonstrate the efficiency of the proposed scheme on relatively coarse meshes. The numerical results indicate that the TFPM achieves high accuracy and effectively captures the shock solutions.

Cited in 5 Documents

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q35 PDEs in connection with fluid mechanics
35K55 Nonlinear parabolic equations

Keywords:

Burgers’ equation; Tailored finite point; Hopf-Cole transformation; viscous flows; explicit scheme
Cite Review PDF
Full Text: DOI

References:

[1] DOI: 10.1016/j.amc.2005.05.020 · Zbl 1090.65108 · doi:10.1016/j.amc.2005.05.020
[2] DOI: 10.1016/j.amc.2010.03.115 · Zbl 1193.65154 · doi:10.1016/j.amc.2010.03.115
[3] DOI: 10.1016/j.amc.2003.11.024 · Zbl 1062.65088 · doi:10.1016/j.amc.2003.11.024
[4] DOI: 10.1016/0045-7825(82)90071-8 · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[5] DOI: 10.1090/qam/42889 · Zbl 0043.09902 · doi:10.1090/qam/42889
[6] DOI: 10.1016/j.amc.2003.08.037 · Zbl 1054.65103 · doi:10.1016/j.amc.2003.08.037
[7] DOI: 10.1016/j.amc.2013.12.035 · Zbl 1364.65207 · doi:10.1016/j.amc.2013.12.035
[8] DOI: 10.1016/0021-9991(81)90207-2 · Zbl 0482.65061 · doi:10.1016/0021-9991(81)90207-2
[9] DOI: 10.1007/s10915-008-9187-7 · Zbl 1203.65221 · doi:10.1007/s10915-008-9187-7
[10] DOI: 10.4208/aamm.2013.m376 · Zbl 1308.65192 · doi:10.4208/aamm.2013.m376
[11] DOI: 10.1016/j.cam.2007.08.014 · Zbl 1149.65079 · doi:10.1016/j.cam.2007.08.014
[12] DOI: 10.1016/j.amc.2004.12.052 · Zbl 1084.65078 · doi:10.1016/j.amc.2004.12.052
[13] DOI: 10.1002/cpa.3160030302 · Zbl 0039.10403 · doi:10.1002/cpa.3160030302
[14] DOI: 10.1007/s10915-011-9468-4 · Zbl 1368.65193 · doi:10.1007/s10915-011-9468-4
[15] DOI: 10.1090/S0025-5718-1987-0906180-5 · doi:10.1090/S0025-5718-1987-0906180-5
[16] DOI: 10.1016/S0377-0427(98)00261-1 · Zbl 0942.65094 · doi:10.1016/S0377-0427(98)00261-1
[17] DOI: 10.1016/j.cam.2003.09.043 · Zbl 1052.65094 · doi:10.1016/j.cam.2003.09.043
[18] DOI: 10.1080/00207160.2010.548519 · Zbl 1252.65141 · doi:10.1080/00207160.2010.548519
[19] DOI: 10.1016/j.amc.2009.08.018 · Zbl 1178.65103 · doi:10.1016/j.amc.2009.08.018
[20] DOI: 10.1007/s10915-010-9354-5 · Zbl 1203.65151 · doi:10.1007/s10915-010-9354-5
[21] DOI: 10.1007/s10915-010-9433-7 · Zbl 1217.65211 · doi:10.1007/s10915-010-9433-7
[22] DOI: 10.1002/cnm.850 · Zbl 1370.35241 · doi:10.1002/cnm.850
[23] DOI: 10.1016/j.amc.2012.06.064 · Zbl 1288.65129 · doi:10.1016/j.amc.2012.06.064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.