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Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional kdv equation

Chinese Physics B 2011年第4期20卷 149-155页

作者： Sayed A.El-Wakil Essam M.Abulwafa Emad K.El-Shewy Abeer A.Mahmoud Theoretical Physics Research Group Physics DepartmentFaculty of ScienceMansoura University

The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional kdv equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional kdv equation is used in a similar form to the Lagrangian of the regular kdv equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional kdv equation. The variational-iteration method is used to solve the derived time fractional kdv equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the kdv equation. The results of the present investigation may be applicable to some plasma environments, such as the ionosphere plasma.

关键词： ion-acoustic waves Euler-Lagrange equation Riemann-Liouvulle fractional derivative fractional kdv equation variational-iteration method

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L1 scheme on graded mesh for the linearized time fractional kdv equation with initial singularity

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第1期10卷 77-94页

作者： Hu Chen Xiaohan Hu Jincheng Ren Tao Sun Yifa Tang Applied and Computational Mathematics Division Beijing Computational Science Research Center Beijing 100194 P.R.China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 P.R.China College of Mathematics and Information Science Henan University of Economics and Law Zhengzhou 450045 P.R.China School of Statistics and Mathematics Shanghai Lixin University of Accounting and Finance Shanghai 201209 P.R.China LSEC ICMSECAcademy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190P.R.China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049P.R.China

Numerical approximation for a linearized time fractional kdv equation with initial singularity using L1 scheme on graded mesh is considered.It is proved that the L1 scheme can attain order 2−αconvergence rate with appropriate choice of the grading parameter,whereα(0fractional derivative.A fully discrete spectral scheme is constructed combing a Petrov-Galerkin spectral method for the spatial discretization,and its stability and convergence are theoretically proved.Some numerical results are provided to verify the theoretical analysis and demonstrated the sharpness of the error analysis.

关键词： fractional kdv equation initial singularity L1 scheme graded mesh

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