Abstract
In this article, a special point is found for the interpolation approximation of the linear combination of multi-term fractional derivatives. The derived numerical differentiation formula can achieve at least second order accuracy. Then the formula is used to numerically solve the time multi-term and distributed-order fractional sub-diffusion equations. Several unconditionally stable and convergent difference schemes are presented. The stability and convergence of the difference schemes are discussed. Some numerical examples are provided to show the efficiency of the proposed difference schemes.
| Original language | English |
|---|---|
| Pages (from-to) | 93-121 |
| Number of pages | 29 |
| Journal | Journal of Scientific Computing |
| Volume | 73 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Oct 2017 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2017, Springer Science+Business Media New York.
Keywords
- Convergence
- Difference scheme
- Distributed-order equation
- Interpolation approximation
- Multi-term fractional derivatives
- Stability
ASJC Scopus subject areas
- Software
- Theoretical Computer Science
- Numerical Analysis
- General Engineering
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics
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