文章基本信息

标题：A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions
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作者：Nauman Khalid ; Muhammad Abbas ; 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：1-22
DOI：10.1186/s13662-020-02616-x
出版社：Hindawi Publishing Corporation
摘要：We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen–Cahn equation (ACE). We discretize the time fractional derivative of order $\alpha\in(0,1]$ by using finite forward difference formula and bring RCBS functions into action for spatial discretization. We find that the numerical scheme is of order $O(h^,+\Delta t^{2-\alpha})$ and unconditionally stable. We test the computational efficiency of the proposed method through some numerical examples subject to homogeneous/nonhomogeneous boundary constraints. The simulation results show a superior agreement with the exact solution as compared to those found in the literature.
关键词：Redefined cubic B-spline functions;Time fractional Allen–Cahn equation;Caputo’s time fractional derivative;Stability and convergence;Finite difference formulation;