Numerical Analysis of the Fractional Seventh-Order KdV Equation Using an Implicit Fully Discrete Local Discontinuous Galerkin Method
Year: 2013
Author: L. Wei, Y. He, Y. Zhang
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 430–444
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-576
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 430–444
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Time-fractional partial differential equations Seventh-order KdV equation Local discontinuous Galerkin method Stability Error estimates.