TY - JOUR
T1 - Numerical Analysis of the Fractional Seventh-Order KdV Equation Using an Implicit Fully Discrete Local Discontinuous Galerkin Method
AU - Wei , L.
AU - He , Y.
AU - Zhang , Y.
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 430
EP - 444
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/576.html
KW - Time-fractional partial differential equations, Seventh-order KdV equation, Local discontinuous Galerkin method, Stability, Error estimates.
AB - <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>