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Numerical simulations of 2D fractional subdiffusion problems. (English) Zbl 1197.65143
Summary: 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.
65M70Spectral, collocation and related methods (IVP of PDE)
35K05Heat equation
35R11Fractional partial differential equations
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