@Article{IJNAM-10-430,
author = {Wei , L.He , Y. and Zhang , Y.},
title = {Numerical Analysis of the Fractional Seventh-Order KdV Equation Using an Implicit Fully Discrete Local Discontinuous Galerkin Method},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {2},
pages = {430--444},
abstract = {<p style="text-align: justify;">In this paper an implicit fully discrete local discontinuous Galerkin (LDG) finite
element method is applied to solve the time-fractional seventh-order Korteweg-de Vries (sKdV)
equation, which is introduced by replacing the integer-order time derivatives with fractional derivatives.
We prove that our scheme is unconditional stable and $L^2$ error estimate for the linear case
with the convergence rate $O(h^{k+1}+(\Delta t)^2+(\Delta t)^{\frac{\alpha}{2}}h^{k+\frac{1}{2}})$ through analysis. Extensive numerical
results are provided to demonstrate the performance of the present method.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/576.html}
}