文章基本信息

标题：Numerical Solution of the Anomalous Diffusion Equation in a Rectangular Domain via Hypermatrix Equations
本地全文：下载
作者：Matthew Harker ; Paul O’Leary
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2017
卷号：50
期号：1
页码：9730-9735
DOI：10.1016/j.ifacol.2017.08.2176
语种：English
出版社：Elsevier
摘要：AbstractThis paper presents a fundamentally new approach to the numerical solution of partial fractional differential equations (PFDE) in higher dimensions by means of hypermatrix equations. By generalizing matrices to their higher dimensional form, i.e., hypermatrices, we show that there is a one-to-one correspondence between PFDE and hypermatrix equations. It is shown that the resulting hypermatrix equation can be solved in an expedient manner, namely by anO(n4) algorithm for anlxmxndiscretized integral surface withl~m~n. Given that previous algorithms were of orderO(n9) this represents a massive improvement in computational complexity. The proposed algorithm is demonstrated for a problem in two spatial and one time dimension; however, the algorithm can be extended to higher dimensions as well.
关键词：KeywordsFractional Order SystemsPartial Fractional Differential EquationFractional DerivativeHypermatrixMatrix EquationsNumerical Approximation