A New Spectral Method Using Nonstandard Singular Basis Functions for Time-Fractional Diferential Equations

doi:10.1007/s42967-019-00012-1

Abstract

Abstract: In this paper, we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial diferential equations (PDEs). Diferent from many other approaches, the nonstandard singular basis functions are defned from some generalised Birkhof interpolation problems through explicit inversion of some prototypical fractional initial value problem (FIVP) with a smooth source term. As such, the singularity of the new basis can be tailored to that of the singular solutions to a class of time-fractional PDEs, leading to spectrally accurate approximation. It also provides the acceptable solution to more general singular problems.

Key words: Fractional diferential equations, Generalised Birkhof interpolation, Nonstandard singular basis functions

CLC Number:

Wenjie Liu, Li-Lian Wang, Shuhuang Xiang. A New Spectral Method Using Nonstandard Singular Basis Functions for Time-Fractional Diferential Equations[J]. Communications on Applied Mathematics and Computation, 2019, 1(2): 207-230.

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