Solving time fractional Burgers’ and Fisher’s equations using cubic B-spline approximation method

This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L 1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank–Nicolson scheme based on cubic B-spline...

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Bibliographic Details
Published in:Advances in difference equations 2020-04, Vol.2020 (1), p.1-15, Article 175
Main Authors: Majeed, Abdul, Kamran, Mohsin, Iqbal, Muhammad Kashif, Baleanu, Dumitru
Format: Article
Language:English
Subjects:
Algorithms
Analysis
B spline functions
Caputo’s fractional derivative
Cubic B-spline collocation method
Difference and Functional Equations
Finite difference formulation
Finite element method
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear programming
Norms
Numerical analysis
Ordinary Differential Equations
Partial Differential Equations
Stability and convergence
Time fractional differential equation
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Summary:This article presents a numerical algorithm for solving time fractional Burgers’ and Fisher’s equations using cubic B-spline finite element method. The L 1 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 2 and L ∞ have been calculated to validate the efficiency and accuracy of the presented algorithm.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02619-8