Numerical Solution of Time Fractional Burgers Equation by Cubic B-spline Finite Elements

Esen, Alaattin; Taşbozan, Orkun

doi:10.1007/s00009-015-0555-x

Cited by 75 publications

(56 citation statements)

References 17 publications

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“…For the fractional Burgers equation we substitute (12), (11) and (8) into (6), and discretize the results at the collocation points x l = l−0.5 m , l = 1, 2, ..., m where m = 2 s−1 M. Hence we get a system of algebraic equations:…”

Section: Methods Of Solutionmentioning

confidence: 99%

A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation

Oruç¹,

Esen²,

Bulut³

2019

Discrete &Amp; Continuous Dynamical Systems - S

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In this paper, we developed a unified method to solve time fractional Burgers' equation using the Chebyshev wavelet and L1 discretization formula. First we give the preliminary information about Chebyshev wavelet method, then we describe time discretization of the problems under consideration and then we apply Chebyshev wavelets for space discretization. The performance of the method is shown by three test problems and obtained results compared with other results available in literature.

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Section: Methods Of Solutionmentioning

confidence: 99%

A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation

Oruç¹,

Esen²,

Bulut³

2019

Discrete &Amp; Continuous Dynamical Systems - S

Self Cite

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“…In the recent literature, various types of fractional versions of the classical Burgers' equation were taken into account from different perspectives, see e.g. [15,8,3,20,7,17,21] and the references therein (in this paper, we also propose a simple motivation for equation (1.2) in Section 5). When α = 1, equation (1.2) reduces to the classical inviscid Burgers' equation…”

Section: Introductionmentioning

confidence: 99%

Singularity Formation in Fractional Burgers’ Equations

et al. 2020

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“…A cubic parametric spline based numerical technique has been developed in [13] for the solution of time fractional Burgers' equation. Cubic B-spline finite elements have been utilized in [14] to develop a numerical technique for the solutions of time fractional Burgers' equation.…”

Section: Introductionmentioning

confidence: 99%

An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers' equation

Yaseen

Abbas

2019

International Journal of Computer Mathematics

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This paper presents a linear computational technique based on cubic trigonometric cubic B-splines for time fractional burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient and significantly reduces the computational cost. The usual finite difference formulation is used to approximate the Caputo time fractional derivative while the derivative in space is discretized using cubic trigonometric B-spline functions. The method is proved to be globally unconditionally stable. To measure the accuracy of the solution, a convergence analysis is also provided. A convergence analysis is Computational experiments are performed to further establish the accuracy and stability of the method. Numerical results are compared with those obtained by a scheme based on parametric spline functions. The comparison reveal that the proposed scheme is quite accurate and effective.

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Numerical Solution of Time Fractional Burgers Equation by Cubic B-spline Finite Elements

Cited by 75 publications

References 17 publications

A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation

A unified finite difference Chebyshev wavelet method for numerically solving time fractional Burgers' equation

Singularity Formation in Fractional Burgers’ Equations

An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers' equation

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