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Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients

  • Zeting Liu EMAIL logo and Shujuan Lü
Published/Copyright: May 24, 2017

Abstract:

We consider the initial value problem of the time fractional diffusion equation on the whole line and the fractional derivative is described in Caputo sense. A fully discrete Hermite pseudospectral approximation scheme is structured basing Hermite-Gauss points in space and finite difference in time. Unconditionally stability and convergence are proved. Numerical experiments are presented and the results conform to our theoretical analysis.

MSC 2010: 35R11; 65M06; 65M70

Funding statement: This work is supported by the NSF of China (No. 11272024 and No. 11672011).

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Received: 2016-8-15
Accepted: 2017-5-4
Published Online: 2017-5-24
Published in Print: 2017-7-26

© 2017 Walter de Gruyter GmbH, Berlin/Boston

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