Lin, Yumin; Xu, Chuanju Finite difference/spectral approximations for the time-fractional diffusion equation. (English) Zbl 1126.65121 J. Comput. Phys. 225, No. 2, 1533-1552 (2007). Consider the problem of finding a numerical solution for the time-fractional diffusion equation with the fractional derivative with respect to time being given in the sense of Caputo. For the solution of this problem, the authors propose a method based on a finite difference scheme with respect to time combined with a Legendre spectral method for the space variable(s). A proof of stability and convergence of the algorithm is provided. Error estimates and numerical results are given as well. Reviewer: Kai Diethelm (Braunschweig) Cited in 4 ReviewsCited in 928 Documents MSC: 65R20 Numerical methods for integral equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 45K05 Integro-partial differential equations 26A33 Fractional derivatives and integrals 35K15 Initial value problems for second-order parabolic equations Keywords:Caputo derivative; time-fractional diffusion equation; finite difference method; spectral method; stability; convergence; numerical results PDFBibTeX XMLCite \textit{Y. Lin} and \textit{C. Xu}, J. Comput. Phys. 225, No. 2, 1533--1552 (2007; Zbl 1126.65121) Full Text: DOI References: [1] Agrawal, O. 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