Neural network method for solving fractional diffusion equations

Haidong Qu, Zihang She and Xuan Liu

Applied Mathematics and Computation, 2021, vol. 391, issue C

Abstract: In this paper, neural networks based on Legendre polynomials are established to solve space and time fractional diffusion equations. The error functions containing adjustable parameters (the weights) for the training sets are constructed. The range of learning rate is analyzed to ensure that the error decreases with respect to training times. Several numerical examples including numerical results and graphs are illustrated. The results show that more training can achieve high precision.

Keywords: Fractional diffusion equation; Neural network method; Time fractional derivative; Space fractional derivative; Time-space fractional derivative (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320305890

DOI: 10.1016/j.amc.2020.125635

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