Abstract
The growing number of applications of fractional derivatives in various fields of science and engineering indicates that there is a significant demand for better mathematical algorithms for models with real objects and processes. Currently, most algorithms are designed for 1D problems due to the memory effect in fractional derivatives. In this work, the 2D fractional subdiffusion problems are solved by an algorithm that couples an adaptive time stepping and adaptive spatial basis selection approach. The proposed algorithm is also used to simulate a subdiffusion-convection equation.
| Original language | English |
|---|---|
| Pages (from-to) | 6613-6622 |
| Number of pages | 10 |
| Journal | Journal of Computational Physics |
| Volume | 229 |
| Issue number | 18 |
| DOIs | |
| Publication status | Published - Sep 2010 |
Scopus Subject Areas
- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Adaptive greedy algorithm
- Collocation
- Fractional differential equations
- Geometric time grids
- Kansa's method
- Radial basis functions