Numerical simulations of 2D fractional subdiffusion problems

Authors:
Hermann Brunner;Leevan Ling;Masahiro Yamamoto
Affiliations:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, Japan
Venue:
Journal of Computational Physics
Year:
2010

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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.