Abbas, MuhammadIqbal, Muhammad KashifBaleanu, DumitruKhalid, Nauman2021-01-282025-09-182021-01-282025-09-182020Khalid, Nauman...et al. (2020). "A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions", Advances in Difference Equations, Vol. 2020, No. 1.1687-1847https://doi.org/10.1186/s13662-020-02616-xhttps://hdl.handle.net/20.500.12416/15064Abbas, Dr. Muhammad/0000-0002-0491-1528; Iqbal, Muhammad Kashif/0000-0003-4442-7498We 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 is an element of (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(h2+Delta t2-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.eninfo:eu-repo/semantics/openAccessRedefined Cubic B-Spline FunctionsTime Fractional Allen-Cahn EquationCaputo'S Time Fractional DerivativeStability And ConvergenceFinite Difference FormulationArticle10.1186/s13662-020-02616-x2-s2.0-85083512717