Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902612 | Applied Numerical Mathematics | 2018 | 13 Pages |
Abstract
In this paper, a class of new compact difference schemes is presented for solving the fourth-order time fractional sub-diffusion equation of the distributed order. By using an effective numerical quadrature rule based on boundary value method to discretize the integral term in the distributed-order derivative, the original distributed order differential equation is approximated by a multi-term time fractional sub-diffusion equation, which is then solved by a compact difference scheme. It is shown that the suggested compact difference scheme is stable and convergent in Lâ norm with the convergence order O(Ï2+h4+(Îγ)p) when a boundary value method of order p is used, where Ï,h and Îγ are the step sizes in time, space and distributed-order variables, respectively. Numerical results are reported to verify the high order accuracy and efficiency of the suggested scheme. Moreover, in the example, comparisons between some existing methods and the suggested scheme is also provided, showing that our method doesn't compromise in computational time.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Maohua Ran, Chengjian Zhang,