A Numerical Investigation of Caputo Time Fractional Allen-Cahn Equation Using Redefined Cubic B-Spline Functions
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Date
2020
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Springer
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GOLD
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Abstract
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 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.
Description
Abbas, Dr. Muhammad/0000-0002-0491-1528; Iqbal, Muhammad Kashif/0000-0003-4442-7498
Keywords
Redefined Cubic B-Spline Functions, Time Fractional Allen-Cahn Equation, Caputo'S Time Fractional Derivative, Stability And Convergence, Finite Difference Formulation, Stability and convergence, Numerical Analysis, Time-Fractional Diffusion Equation, Statistical and Nonlinear Physics, Time fractional Allen–Cahn equation, Computer science, Finite difference formulation, Algorithm, Fractional Derivatives, Physics and Astronomy, Numerical Methods for Singularly Perturbed Problems, Modeling and Simulation, Physical Sciences, QA1-939, FOS: Mathematics, Redefined cubic B-spline functions, Fractional Calculus, Finite Difference Schemes, Anomalous Diffusion Modeling and Analysis, Mathematics, Caputo’s time fractional derivative, Rogue Waves in Nonlinear Systems, redefined cubic B-spline functions, Fractional derivatives and integrals, Fractional partial differential equations, finite difference formulation, time fractional Allen-Cahn equation, stability and convergence, Caputo's time fractional derivative, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Fields of Science
01 natural sciences, 0103 physical sciences
Citation
Khalid, 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.
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Q1
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OpenCitations Citation Count
41
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 8
Scopus : 51
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