Proceedings of the 2017 6th International Conference on Measurement, Instrumentation and Automation (ICMIA 2017)

Legendre-Galerkin method for nonlinear partial differential equations

Authors
Jun Liu, Xinyue Fan
Corresponding Author
Jun Liu
Available Online June 2017.
DOI
https://doi.org/10.2991/icmia-17.2017.71How to use a DOI?
Keywords
Legendre-Galerkin method; Burgers equation; Error estimate
Abstract
In this paper, a Legendre-Galerkin method is proposed and analyzed for the Burgers equation with dirichlet boundary condition. We present in this paper the error estimation concerning Legendre approximations in Sobolev spaces, in which integration is performed with respect to the Legendre weight. It is shown that the Legendre-Galerkin approximations are convergent on the interval [-1,1] with spectral accuracy. An efficient and accurate algorithm based on the Legendre-Galerkin approximations to the Burgers equation is developed and implemented. Finally the numerical results which indicate that the high accuracy and effectiveness of this algorithm are presented.
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Proceedings
2017 6th International Conference on Measurement, Instrumentation and Automation (ICMIA 2017)
Part of series
Advances in Intelligent Systems Research
Publication Date
June 2017
ISBN
978-94-6252-387-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/icmia-17.2017.71How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Jun Liu
AU  - Xinyue Fan
PY  - 2017/06
DA  - 2017/06
TI  - Legendre-Galerkin method for nonlinear partial differential equations
BT  - 2017 6th International Conference on Measurement, Instrumentation and Automation (ICMIA 2017)
PB  - Atlantis Press
SN  - 1951-6851
UR  - https://doi.org/10.2991/icmia-17.2017.71
DO  - https://doi.org/10.2991/icmia-17.2017.71
ID  - Liu2017/06
ER  -