Browsing by Author "Mei, Liquan"

Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation
    (2014-06-19) Mei, Liquan; Gao, Yali; Chen, Zhangxin
    A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.
  • Thumbnail Image
    ItemOpen Access
    Existence of Weak Solutions for Nonlinear Time-Fractional -Laplace Problems
    (2014-07-02) Qiu, Meilan; Mei, Liquan
    The existence of weak solution for -Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the Nehari manifold, the existence of weak solutions is established. By means of the Arzela-Ascoli fixed point theorem, some existence results of the corresponding time-fractional equations of the -Laplace problem are obtained.