Department of Mathematics
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
Journal of Computational Physics
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Last Page (page number)
Fractional differential equations, Kansa’s method, radial basis functions, collocation, adaptive greedy algorithm, geometric time grids
Brunner, Hermann, L. Ling, and Masahiro Yamamoto. "Numerical simulations of two-dimensional fractional subdiffusion problems." Journal of Computational Physics 229.18 (2010): 6613-6622.