Numerical treatment of fractional heat equations

Authors:
R. Scherer;S. L. Kalla;L. Boyadjiev;B. Al-Saqabi
Affiliations:
Institute of Applied and Numerical Mathematics, Universität Karlsruhe (TH), D-76128 Karlsruhe, Germany;Department of Mathematics, Kuwait University, Kuwait;Department of Applied Mathematics and Informatics, Technical University, Sofia, Bulgaria;Department of Mathematics, Kuwait University, Kuwait
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

This paper is devoted to the numerical treatment of some fractional extensions of the temperature field problem in oil strata. Based on the Grunwald-Letnikov's definition of a fractional derivative, finite difference schemes for the approximation of the solution are discussed. By means of them the fractional heat equation is solved. The main properties of the explicit and implicit numerical methods developed, related to stability, convergence and error behaviour are also studied. Stability conditions as extensions of the CLF condition are derived and numerical experiments are provided.