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Volume 10, Issue 2
Numerical Analysis of the Fractional Seventh-Order KdV Equation Using an Implicit Fully Discrete Local Discontinuous Galerkin Method

L. Wei, Y. He & Y. Zhang

Int. J. Numer. Anal. Mod., 10 (2013), pp. 430-444.

Published online: 2013-10

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  • 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.

  • Keywords

Time-fractional partial differential equations, Seventh-order KdV equation, Local discontinuous Galerkin method, Stability, Error estimates.

  • AMS Subject Headings

65M60, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/576.html} }
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 -

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.

Wei , L.He , Y. and Zhang , Y.. (2013). Numerical Analysis of the Fractional Seventh-Order KdV Equation Using an Implicit Fully Discrete Local Discontinuous Galerkin Method. International Journal of Numerical Analysis and Modeling. 10 (2). 430-444. doi:
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