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

作　　者：Wenjie Liu Li-Lian Wang Shuhuang Xiang 

机构地区：[1]Department of Mathematics,Harbin Institute of Technology,Harbin 150001,China [2]Division of Mathematical Sciences,School of Physical and Mathematical Sciences,Nanyang Technological University,Singapore 637371,Singapore [3]Mathematics and Statistics,Central South University,Changsha 410083,China

出　　处：《Communications on Applied Mathematics and Computation》2019年第2期207-230,共24页应用数学与计算数学学报（英文）

基　　金：the China Postdoctoral Science Foundation Funded Project (No.2017M620113);the National Natural Science Foundation of China (Nos.11801120,71773024 and 11771107);the Fundamental Research Funds for the Central Universities (Grant No.HIT.NSRIF.2019058);the Natural Science Foundation of Heilongjiang Province of China (No.G2018006);Singapore MOE AcRF Tier 2 Grants (MOE2017-T2-2-014 and MOE2018-T2-1-059);National Science Foundation of China (No.11371376);the Innovation-Driven Project and Mathematics.

摘　　要：In this paper,we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial differential equations (PDEs). Different from many other approaches,the nonstandard singular basis functions are defined from some generalised Birkhoff 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.

关 键 词：FRACTIONAL differential equations Generalised BIRKHOFF interpolation NONSTANDARD SINGULAR basis function 

分 类 号：O1[理学—数学]