Legendre-Galerkin method for nonlinear partial differential equations

DOI

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.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jun Liu
AU  - Xinyue Fan
PY  - 2017/06
DA  - 2017/06
TI  - Legendre-Galerkin method for nonlinear partial differential equations
BT  - Proceedings of the 2017 6th International Conference on Measurement, Instrumentation and Automation (ICMIA 2017)
PB  - Atlantis Press
SP  - 391
EP  - 401
SN  - 1951-6851
UR  - https://doi.org/10.2991/icmia-17.2017.71
DO  - 10.2991/icmia-17.2017.71
ID  - Liu2017/06
ER  -