Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method |
| |
| Authors: | Leilei Wei Yinnian He Bo Tang |
| |
| Affiliation: | 1. Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China;2. Department of Mathematics, Luoyang Normal University, Luoyang 471022, People's Republic of China |
| |
| Abstract: | In this article, an implicit fully discrete local discontinuous Galerkin (LDG) finite element method, on the basis of finite difference method in time and LDG method in space, is applied to solve the time‐fractional Kawahara equation, which is introduced by replacing the integer‐order time derivatives with fractional derivatives. We prove that our scheme is unconditional stable and convergent through analysis. Extensive numerical results are provided to demonstrate the performance of the present method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 |
| |
| Keywords: | error estimates local discontinuous Galerkin method stability the Kawahara equation time‐fractional partial differential equations |
|
|
