Abstract
This article is concerned with ?-methods for delay parabolic partial differential equations. The methodology is extended to time-fractional-order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay-independent asymptotic stability and the solution continuously depends on the time-fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method.
Original language | English |
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Pages (from-to) | 1556-1571 |
Number of pages | 16 |
Journal | Numerical Methods for Partial Differential Equations |
Volume | 26 |
Issue number | 6 |
DOIs | |
Publication status | Published - Nov 2010 |
Keywords
- ?-methods
- Diffusion equations
- Discretization
- Fractional derivative order
- Runke-Kutta
- Stability regions
- Stiffness
- Time-lag
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics