Legendre-Galerkin method for nonlinear partial differential equations
Jun Liu, Xinyue Fan
Available Online June 2017.
- https://doi.org/10.2991/icmia-17.2017.71How to use a DOI?
- Legendre-Galerkin method; Burgers equation; Error estimate
- 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.
- 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 -