Numerical analysis and physical simulations for the time fractional radial diffusion equation |
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Authors: | Can Li Weihua Deng Yujiang Wu |
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Affiliation: | School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China |
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Abstract: | We do the numerical analysis and simulations for the time fractional radial diffusion equation used to describe the anomalous subdiffusive transport processes on the symmetric diffusive field. Based on rewriting the equation in a new form, we first present two kinds of implicit finite difference schemes for numerically solving the equation. Then we strictly establish the stability and convergence results. We prove that the two schemes are both unconditionally stable and second order convergent with respect to the maximum norm. Some numerical results are presented to confirm the rates of convergence and the robustness of the numerical schemes. Finally, we do the physical simulations. Some interesting physical phenomena are revealed; we verify that the long time asymptotic survival probability ∝t−α, but independent of the dimension, where α is the anomalous diffusion exponent. |
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Keywords: | Finite difference approach Time fractional radial diffusion equation Stability Convergence Simulation |
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