000191320 001__ 191320
000191320 005__ 20190316235755.0
000191320 0247_ $$2doi$$a10.1016/j.jcp.2014.10.016
000191320 022__ $$a0021-9991
000191320 02470 $$2ISI$$a000354119500014
000191320 037__ $$aARTICLE
000191320 245__ $$aA Multi-domain Spectral Method for Time-fractional Differential Equations
000191320 269__ $$a2015
000191320 260__ $$bElsevier$$c2015$$aSan Diego
000191320 300__ $$a16
000191320 336__ $$aJournal Articles
000191320 520__ $$aThis 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.
000191320 6531_ $$amulti-domain
000191320 6531_ $$aspectral
000191320 6531_ $$atime-fractional
000191320 6531_ $$ahigh-orderintegration
000191320 6531_ $$athree-term-recurrence
000191320 6531_ $$ageneral linear method
000191320 700__ $$aChen, Feng
000191320 700__ $$aXu, Qinwu
000191320 700__ $$g232231$$aHesthaven, Jan S.$$0247428
000191320 773__ $$j293$$tJournal of Computational Physics$$q157-172
000191320 8564_ $$uhttps://infoscience.epfl.ch/record/191320/files/main.pdf$$zPreprint$$s1183960$$yPreprint
000191320 909C0 $$xU12703$$0252492$$pMCSS
000191320 909CO $$qGLOBAL_SET$$pSB$$ooai:infoscience.tind.io:191320$$particle
000191320 917Z8 $$x232231
000191320 917Z8 $$x232231
000191320 937__ $$aEPFL-ARTICLE-191320
000191320 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000191320 980__ $$aARTICLE