文章基本信息

标题：A collocation method based on cubic trigonometric B-splines for the numerical simulation of the time-fractional diffusion equation
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作者：Muhammad Yaseen ; Muhammad Abbas ; Muhammad Bilal Riaz 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2021
卷号：2021
期号：1
页码：1
DOI：10.1186/s13662-021-03360-6
出版社：Hindawi Publishing Corporation
摘要：Fractional differential equations sufficiently depict the nature in view of the symmetry properties, which portray physical and biological models. In this paper, we present a proficient collocation method based on cubic trigonometric B-Splines (CuTBSs) for time-fractional diffusion equations (TFDEs). The methodology involves discretization of the Caputo time-fractional derivatives using the typical finite difference scheme with space derivatives approximated using CuTBSs. A stability analysis is performed to establish that the errors do not magnify. A convergence analysis is also performed The numerical solution is obtained as a piecewise sufficiently smooth continuous curve, so that the solution can be approximated at any point in the given domain. Numerical tests are efficiently performed to ensure the correctness and viability of the scheme, and the results contrast with those of some current numerical procedures. The comparison uncovers that the proposed scheme is very precise and successful.
关键词：Time-fractional diffusion equation ; Cubic trigonometric B-spline method ; Spline approximations ; Stability ; Convergence