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

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}+(Δt)^2+(Δt)^{\frac{α}{2}}h^{k+\frac12}) 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

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@Article{IJNAM-10-430, author = {L. Wei and Y. He}, 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}+(Δt)^2+(Δt)^{\frac{α}{2}}h^{k+\frac12}) 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 - L. Wei & Y. He 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 KW - Seventh-order KdV equation KW - Local discontinuous Galerkin method KW - Stability KW - 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}+(Δt)^2+(Δt)^{\frac{α}{2}}h^{k+\frac12}) through analysis. Extensive numerical results are provided to demonstrate the performance of the present method.
L. Wei & Y. He. (1970). 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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