A numerical investigation of the time distributed-order diffusion model

Xiuling Hu, Fawang Liu, Vo Anh, Ian Turner


Distributed-order differential models are more powerful tools to describe complex dynamical systems than the classical and fractional-order models because of their nonlocal properties. A time distributed-order diffusion model is investigated. By employing some numerical integration techniques, we approximate the distributed-order fractional model with a multi-term fractional model, which is then solved by an implicit numerical method. The stability and convergence of the numerical method is analyzed. Some numerical results are presented to demonstrate the effectiveness of the method and to exhibit the solution behavior of three different diffusion models.

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time distributed-order diffusion model; multi-term fractional model;implicit numerical method; Stability and convergence

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DOI: http://dx.doi.org/10.21914/anziamj.v55i0.7888

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