A finite difference method with non-uniform timesteps for fractional diffusion and diffusion-wave equations

@inproceedings{QuintanaMurillo2013AFD,
  title={A finite difference method with non-uniform timesteps for fractional diffusion and diffusion-wave equations},
  author={Joaqu{\'i}n Quintana-Murillo and Santos B. Yuste},
  year={2013}
}
An implicit finite difference method with non-uniform timesteps for solving fractional diffusion and diffusion-wave equations in the Caputo form is presented. The non-uniformity of the timesteps allows one to adapt their size to the behaviour of the solution, which leads to large reductions in the computational time required to obtain the numerical solution without loss of accuracy. The stability of the method has been proved recently for the case of diffusion equations; for diffusion-wave… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 12 extracted citations

References

Publications referenced by this paper.
Showing 1-7 of 7 references

Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications

I. Podlubny
1999
View 3 Excerpts
Highly Influenced

J

K. B. Oldham
Spanier, The Fractional Calculus (Academic Press, New York, • 1974
View 3 Excerpts
Highly Influenced

Discretization of fractionalorder operators and fractional differential equations on a non-equidistant mesh

T. Skovranek, V. V. Verbickij, Y. Tarte, I. Podlubny
Article no. FDA10-062, • 2010

G

R. Klages
Radons, I.M. Sokolov (eds.), Anomalous Transport: Foundations and Applications (Elsevier, Amsterdam, • 2008
View 1 Excerpt

Phys

B. I. Henry, T.A.M. Langlands, S. Wearne
Rev. Lett. 100, 128103 (2008) • 1998

Similar Papers

Loading similar papers…