@Article{IJNAM-10-2,
author = {Wei, L. and Y., He 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/2013-IJNAM-576},
url = {https://global-sci.com/article/83405/numerical-analysis-of-the-fractional-seventh-order-kdv-equation-using-an-implicit-fully-discrete-local-discontinuous-galerkin-method}
}