文章基本信息

标题：A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation
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作者：Muhammad Yaseen ; Muhammad Abbas ; Tahir Nazir 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：2017
卷号：2017
期号：1
页码：1-18
DOI：10.1186/s13662-017-1330-z
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we propose an efficient numerical scheme for the approximate solution of a time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is approximated by the usual finite difference formulation, and the derivative in space is discretized using cubic trigonometric B-spline functions. A stability analysis of the scheme is conducted to confirm that the scheme does not amplify errors. Computational experiments are also performed to further establish the accuracy and validity of the proposed scheme. The results obtained are compared with finite difference schemes based on the Hermite formula and radial basis functions. It is found that our numerical approach performs superior to the existing methods due to its simple implementation, straightforward interpolation and very low computational cost. A convergence analysis of the scheme is also discussed.
关键词：time fractional diffusion-wave equation;trigonometric basis functions;cubic trigonometric B-splines method;stability