Chen, FengXu, QinwuHesthaven, Jan S.2013-12-172013-12-172013-12-17201510.1016/j.jcp.2014.10.016https://infoscience.epfl.ch/handle/20.500.14299/97997WOS:000354119500014This 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.multi-domainspectraltime-fractionalhigh-orderintegrationthree-term-recurrencegeneral linear methodtext::journal::journal article::research article