文章基本信息

标题：Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method
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作者：Abdul Majeed ; Mohsin Kamran ; Muhammad Kashif Iqbal 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：2020
卷号：2020
期号：1
页码：1-15
DOI：10.1186/s13662-020-02619-8
出版社：Hindawi Publishing Corporation
摘要：This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank–Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers’ and Fisher’s equations. The error norms $L_,$ and $L_{\infty }$ have been calculated to validate the efficiency and accuracy of the presented algorithm.
关键词：Cubic B-spline collocation method;Time fractional differential equation;Caputo’s fractional derivative;Stability and convergence;Finite difference formulation;