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A compact Crank–Nicholson scheme for the numerical solution of fuzzy time fractional diffusion equations

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Abstract

Fuzzy fractional partial differential equations are a generalization of classical fuzzy partial differential equation which can, in certain circumstances, provide a better explanation for certain phenomena. In this paper, a compact Crank–Nicholson scheme is developed, analyzed and applied to solve the fuzzy time diffusion equation with fractional order \(0 < \alpha \le 1\). It is based on double parametric form of fuzzy numbers and the time fractional derivative is defined using the Caputo definition. The truncation error and stability of the proposed scheme is discussed. The compact Crank–Nicholson scheme is shown to be a feasible scheme via a numerical example.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Pulau Pinang, Malaysia

    Hamzeh Zureigat, Ahmad Izani Ismail & Saratha Sathasivam

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  1. Hamzeh Zureigat
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  2. Ahmad Izani Ismail
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  3. Saratha Sathasivam
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Correspondence to Hamzeh Zureigat.

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Zureigat, H., Ismail, A.I. & Sathasivam, S. A compact Crank–Nicholson scheme for the numerical solution of fuzzy time fractional diffusion equations. Neural Comput & Applic 32, 6405–6412 (2020). https://doi.org/10.1007/s00521-019-04148-2

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