Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method
Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method
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DOI：
10.1002/num.21756
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发表时间：
2013-09
影响因子：
3.9
通讯作者：
Leilei Wei;Yinnian He;Bo Tang
中科院分区：
文献类型：
--
作者：
Leilei Wei;Yinnian He;Bo Tang
本文在时间域有限差分法和空间域LDG法的基础上，将时间分数阶Kawahara方程的整数阶时间导数替换为分数阶时间导数，提出了一种求解时间分数阶Kawahara方程的隐式全离散局部间断Galerkin（LDG）有限元方法。通过分析证明了该格式是无条件稳定和收敛的。大量的数值结果证明了本方法的性能。© 2012 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq，2013
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