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Keywords:

  • error estimates;
  • local discontinuous Galerkin method;
  • stability;
  • the Kawahara equation;
  • time-fractional partial differential equations

Abstract

In this article, an implicit fully discrete local discontinuous Galerkin (LDG) finite element method, on the basis of finite difference method in time and LDG method in space, is applied to solve the time-fractional Kawahara equation, which is introduced by replacing the integer-order time derivatives with fractional derivatives. We prove that our scheme is unconditional stable and convergent through analysis. Extensive numerical results are provided to demonstrate the performance of the present method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013