Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1072.65123
Langlands, T.A.M.; Henry, B.I.
The accuracy and stability of an implicit solution method for the fractional diffusion equation.
(English)
[J] J. Comput. Phys. 205, No. 2, 719-736 (2005). ISSN 0021-9991

Summary: We have investigated the accuracy and stability of an implicit numerical scheme for solving the fractional diffusion equation. This model equation governs the evolution for the probability density function that describes anomalously diffusing particles. Anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur. The implicit numerical scheme that we have investigated is based on finite difference approximations and is straightforward to implement. The accuracy of the scheme is $O(\Delta x^2)$ in the spatial grid size and $O(\Delta t^{1 + \gamma})$ in the fractional time step, where $0\leqslant 1 - \gamma < 1$ is the order of the fractional derivative and $\gamma = 1$ is standard diffusion. We have provided algebraic and numerical evidence that the scheme is unconditionally stable for $0 < \gamma \leqslant 1$.
MSC 2000:
*65M12 Stability and convergence of numerical methods (IVP of PDE)
65M06 Finite difference methods (IVP of PDE)
35K05 Heat equation

Keywords: Fractional diffusion equation; von Neumann stability analysis; Anomalous diffusion; finite difference

Cited in: Zbl 1165.65053

Highlights
Master Server