Zhang, Haixiang; Han, Xuli Quasi-wavelet method for time-dependent fractional partial differential equation. (English) Zbl 1284.65194 Int. J. Comput. Math. 90, No. 11, 2491-2507 (2013). The authors present a numerical method for a time-fractional diffusion equation in one space dimension where the order of the time derivative is \(1/2\). The boundary conditions are homogeneous; the initial condition may be inhomogeneous. The equation is given in a slightly non-standard integro-differential form. This is handled by a time discretization that essentially amounts to a finite difference method. After an analysis of stability and convergence properties of the resulting semidiscrete equation, the space variable is discretized via a quasi-wavelet approach based on sinc functions. Some numerical results are given. Reviewer: Kai Diethelm (Braunschweig) Cited in 6 Documents MSC: 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 26A33 Fractional derivatives and integrals Keywords:fractional differential equation; quasi-wavelet; stability; convergence; integro-differential equation; semidiscretization; time-fractional diffusion equation; finite difference method; numerical result PDFBibTeX XMLCite \textit{H. Zhang} and \textit{X. Han}, Int. J. Comput. Math. 90, No. 11, 2491--2507 (2013; Zbl 1284.65194) Full Text: DOI References: [1] DOI: 10.1364/OL.28.000513 · doi:10.1364/OL.28.000513 [2] DOI: 10.1002/nme.883 · Zbl 1043.65132 · doi:10.1002/nme.883 [3] C.K. Chui,An Introduction to Wavelets, Academic Press, Boston, MA, 1992. · Zbl 0925.42016 [4] DOI: 10.1023/A:1016547232119 · Zbl 1009.82016 · doi:10.1023/A:1016547232119 [5] DOI: 10.1016/S0378-4371(99)00469-0 · doi:10.1016/S0378-4371(99)00469-0 [6] DOI: 10.1016/j.cam.2011.01.011 · Zbl 1216.65130 · doi:10.1016/j.cam.2011.01.011 [7] DOI: 10.1016/j.jcp.2007.02.001 · Zbl 1126.65121 · doi:10.1016/j.jcp.2007.02.001 [8] DOI: 10.1137/080718942 · Zbl 1193.35243 · doi:10.1137/080718942 [9] DOI: 10.1016/j.cam.2004.01.033 · Zbl 1126.76346 · doi:10.1016/j.cam.2004.01.033 [10] DOI: 10.1016/j.cam.2009.02.013 · Zbl 1170.65107 · doi:10.1016/j.cam.2009.02.013 [11] DOI: 10.1016/j.amc.2012.04.090 · Zbl 1278.65199 · doi:10.1016/j.amc.2012.04.090 [12] DOI: 10.1007/s11425-010-4133-1 · Zbl 1217.34010 · doi:10.1007/s11425-010-4133-1 [13] DOI: 10.1016/S0370-1573(00)00070-3 · Zbl 0984.82032 · doi:10.1016/S0370-1573(00)00070-3 [14] DOI: 10.1090/S0002-9939-02-06887-9 · Zbl 1018.94004 · doi:10.1090/S0002-9939-02-06887-9 [15] L. Schwarz,Théore des Distributions, Hermann, Paris, 1951. [16] DOI: 10.1016/S0021-9991(03)00226-2 · Zbl 1024.78011 · doi:10.1016/S0021-9991(03)00226-2 [17] DOI: 10.1016/0168-9274(93)90012-G · Zbl 0768.65093 · doi:10.1016/0168-9274(93)90012-G [18] DOI: 10.1006/jcph.2002.7089 · Zbl 1130.76403 · doi:10.1006/jcph.2002.7089 [19] DOI: 10.1016/S0009-2614(98)01061-6 · doi:10.1016/S0009-2614(98)01061-6 [20] DOI: 10.1063/1.478812 · doi:10.1063/1.478812 [21] DOI: 10.1088/0305-4470/33/27/311 · Zbl 0988.82047 · doi:10.1088/0305-4470/33/27/311 [22] DOI: 10.1103/PhysRevLett.79.775 · doi:10.1103/PhysRevLett.79.775 [23] DOI: 10.1006/jsvi.2002.5055 · doi:10.1006/jsvi.2002.5055 [24] DOI: 10.1080/00207160.2011.587003 · Zbl 1243.65165 · doi:10.1080/00207160.2011.587003 [25] DOI: 10.1016/j.jcp.2012.09.037 · Zbl 1284.35454 · doi:10.1016/j.jcp.2012.09.037 [26] DOI: 10.1023/A:1022284616125 · Zbl 1058.65148 · doi:10.1023/A:1022284616125 [27] DOI: 10.1137/S1064827501390972 · Zbl 1043.35015 · doi:10.1137/S1064827501390972 [28] DOI: 10.1016/S0020-7683(01)00241-4 · Zbl 1090.74603 · doi:10.1016/S0020-7683(01)00241-4 [29] DOI: 10.1016/j.jsv.2004.08.037 · Zbl 1237.74198 · doi:10.1016/j.jsv.2004.08.037 [30] DOI: 10.1137/060673114 · Zbl 1173.26006 · doi:10.1137/060673114 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.