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Original Articles

Galerkin–Legendre spectral method for the distributed-order time fractional fourth-order partial differential equation

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Pages 1183-1196 | Received 24 Dec 2018, Accepted 13 Apr 2019, Published online: 27 Apr 2019
 

ABSTRACT

In this paper, we consider the Galerkin–Legendre spectral method for solving the two-dimensional distributed-order time fractional fourth-order partial differential equation. By utilizing the composite Simpson formula to discretize the distributed-order integral, we transform the considered equation into a multi-term time fractional sub-diffusion equation. Then the L2-1σ formula is used to approximate the multi-term Caputo fractional derivatives and the Legendre spectral method is employed for the spatial discretization. The scheme is proved to be unconditionally stable and convergent in both L2- and L-norms with fourth-order accuracy in distributed order, second-order accuracy in time and spectral accuracy in space. Finally, some numerical tests are performed to verify the theoretical results.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Acknowledgements

The authors would like to thank the editor and the referees for their valuable comments and suggestions which helped us improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSF of China (National Natural Science Foundation of China) [No. 11771163].

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