UM  > Faculty of Science and Technology  > DEPARTMENT OF MATHEMATICS
 Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations Liao, Hong-lin1; Lyu, Pin2; Vong, Seakweng2; Zhao, Ying1 2017-08 Source Publication NUMERICAL ALGORITHMS ISSN 1017-1398 Volume 75Issue:4Pages:845-878 Abstract Two fully discrete methods are investigated for simulating the distributed-order sub-diffusion equation in Caputo's form. The fractional Caputo derivative is approximated by the Caputo's BDF1 (called L1 early) and BDF2 (or L1-2 when it was first introduced) approximations, which are constructed by piecewise linear and quadratic interpolating polynomials, respectively. It is shown that the first scheme, using the BDF1 formula, possesses the discrete minimum-maximum principle and nonnegativity preservation property such that it is stable and convergent in the maximum norm. The method using the BDF2 formula is shown to be stable and convergent in the discrete H (1) norm by using the discrete energy method. For problems of distributed order within a certain region, the method is also proven to preserve the discrete maximum principle and nonnegativity property. Extensive numerical experiments are provided to show the effectiveness of numerical schemes, and to examine the initial singularity of the solution. The applicability of our numerical algorithms to a problem with solution which lacks the smoothness near the initial time is examined by employing a class of power-type nonuniform meshes. Keyword Fractional Subdiffusion Equations Caputo Derivative Caputo's Bdf Formulas Minimum-maximum Principle Discrete Energy Method Stability And Convergence DOI 10.1007/s11075-016-0223-7 URL View the original Indexed By SCIE Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000406214300001 Publisher SPRINGER The Source to Article WOS Fulltext Access Citation statistics Cited Times [WOS]:16   [WOS Record]     [Related Records in WOS] Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Affiliation 1.Institute of SciencesPLA University of Science and TechnologyNanjingPeople’s Republic of China2.Department of MathematicsUniversity of MacauMacauChina Recommended CitationGB/T 7714 Liao, Hong-lin,Lyu, Pin,Vong, Seakweng,et al. Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations[J]. NUMERICAL ALGORITHMS,2017,75(4):845-878. APA Liao, Hong-lin,Lyu, Pin,Vong, Seakweng,&Zhao, Ying.(2017).Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations.NUMERICAL ALGORITHMS,75(4),845-878. MLA Liao, Hong-lin,et al."Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations".NUMERICAL ALGORITHMS 75.4(2017):845-878.
 Files in This Item: There are no files associated with this item.
 Related Services Recommend this item Bookmark Usage statistics Export to Endnote Google Scholar Similar articles in Google Scholar [Liao, Hong-lin]'s Articles [Lyu, Pin]'s Articles [Vong, Seakweng]'s Articles Baidu academic Similar articles in Baidu academic [Liao, Hong-lin]'s Articles [Lyu, Pin]'s Articles [Vong, Seakweng]'s Articles Bing Scholar Similar articles in Bing Scholar [Liao, Hong-lin]'s Articles [Lyu, Pin]'s Articles [Vong, Seakweng]'s Articles Terms of Use No data! Social Bookmark/Share