A Multi-domain Spectral Method for Time-fractional Differential Equations

This paper proposes an approach for high-order time integration within a multi-domain setting for time- fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.


Published in:
Journal of Computational Physics, 293, 157-172
Year:
2015
Publisher:
San Diego, Elsevier
ISSN:
0021-9991
Keywords:
Laboratories:




 Record created 2013-12-17, last modified 2018-03-17

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