In this work, we solve distributed order diffusion equations (DODEs) by applying the theory on reproducing kernel functions (RKFs). The classical numerical quadrature formulae is used to approximate the DODE to a mult...
详细信息
In this work, we solve distributed order diffusion equations (DODEs) by applying the theory on reproducing kernel functions (RKFs). The classical numerical quadrature formulae is used to approximate the DODE to a multi-term Caputo fractional orderdiffusion equation (FDE). The Mittag-Leffler RKF is introduced to estimate fractional derivatives of Caputo. And a space-time RKFs collocation scheme is derived for the multi-term Caputo time FDEs. The accuracy of the present numerical technique is indicated by employing several experiments.
In this paper, an effective numerical fully discrete finite element scheme for the distributedorder time fractional diffusionequations is developed. By use of the composite trapezoid formula and the well-known L1 fo...
详细信息
In this paper, an effective numerical fully discrete finite element scheme for the distributedorder time fractional diffusionequations is developed. By use of the composite trapezoid formula and the well-known L1 formula approximation to the distributedorder derivative and linear triangular finite element approach for the spatial discretization, we construct a fully discrete finite element scheme. Based on the superclose estimate between the interpolation operator and the Ritz projection operator and the interpolation post-processing technique, the superclose approximation of the finite element numerical solution and the global superconvergence are proved rigorously, respectively. Finally, a numerical example is presented to support the theoretical results.
In this paper, a numerical fully discrete scheme based on the finite element approximation for the distributedorder time fractional variable coefficient diffusionequations is developed and a complete error analysis ...
详细信息
In this paper, a numerical fully discrete scheme based on the finite element approximation for the distributedorder time fractional variable coefficient diffusionequations is developed and a complete error analysis is provided. The weighted and shifted Grunwald formula is applied for the time-fractional derivative and finite element approach for the spatial discretization. The unconditional stability and the global superconvergence estimate of the fully discrete scheme are proved rigorously. Extensive numerical experiments are presented to illustrate the accuracy and efficiency of the scheme, and to verify the convergence theory.
暂无评论