Abstract
Based on the composite Simpson's quadrature rule and the composite 2-point Gauss-Legendre quadrature rule, 2 high-order finite difference schemes were proposed for solving time distributed-order diffusion equations. Other than the existing methods whose convergence rates are only 1st-order or 2nd-order in the temporal domain, the proposed 2 schemes both have 3rd-order convergence rates in the temporal domain, and 4th-order rates in the spatial domain and the distributed order, respectively. Such high-order convergence rates were further verified with numerical examples. The results show that, both of the proposed 2 schemes are stable, and have higher accuracy and efficiency compared with existing algorithms.
| Translated title of the contribution | Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations |
|---|---|
| Original language | Chinese (Traditional) |
| Pages (from-to) | 791-800 |
| Number of pages | 10 |
| Journal | Applied Mathematics and Mechanics |
| Volume | 40 |
| Issue number | 7 |
| DOIs | |
| State | Published - 1 Jul 2019 |