Solving Time Fractional Burgers' and Fisher's Equations Using Cubic B-Spline Approximation Method
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Date
2020
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Springer
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GOLD
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Abstract
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 L2 and L infinity have been calculated to validate the efficiency and accuracy of the presented algorithm.
Description
Iqbal, Muhammad Kashif/0000-0003-4442-7498
ORCID
Keywords
Cubic B-Spline Collocation Method, Time Fractional Differential Equation, Caputo'S Fractional Derivative, Stability And Convergence, Finite Difference Formulation, Caputo’s fractional derivative, Stability and convergence, Quadrature Formulas, Mathematical analysis, Finite difference formulation, Convergence Analysis of Iterative Methods for Nonlinear Equations, B-spline, QA1-939, FOS: Mathematics, Anomalous Diffusion Modeling and Analysis, Numerical Analysis, Cubic B-spline collocation method, Time-Fractional Diffusion Equation, Statistical and Nonlinear Physics, Applied mathematics, Algorithm, Time fractional differential equation, Fractional Derivatives, Physics and Astronomy, Modeling and Simulation, Physical Sciences, Fractional Calculus, Mathematics, Rogue Waves in Nonlinear Systems, Discretization, Numerical computation using splines, cubic B-spline collocation method, time fractional differential equation, Caputo's fractional derivative, Fractional partial differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, finite difference formulation, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, stability and convergence, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
Turkish CoHE Thesis Center URL
Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
Citation
Majeed, Abdul...et al. (2020) "Solving time fractional Burgers' and Fisher's equations using cubic B-spline approximation method", Advances in Difference Equations, Vol. 2020, No. 1.
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Q1
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OpenCitations Citation Count
42
Source
Advances in Difference Equations
Volume
2020
Issue
1
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CrossRef : 25
Scopus : 60
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