Numerical and exact solutions for time fractional Burgers' equation
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Authors
Asıf Yokuş
- Department of Actuary, Firat University, Elazig, Turkey.
Doğan Kaya
- Department of Mathematics, Istanbul Commerce University, Istanbul, Turkey.
Abstract
The main purpose of this paper is to find an exact solution of the traveling wave equation of a nonlinear time fractional
Burgers’ equation using the expansion method and the Cole-Hopf transformation. For this purpose, a nonlinear time fractional
Burgers’ equation with the initial conditions considered. The finite difference method (FDM for short) which is based on the
Caputo formula is used and some fractional differentials are introduced. The Burgers’ equation is linearized by using the Cole-
Hopf transformation for a stability of the FDM. It shows that the FDM is stable for the usage of the Fourier-Von Neumann
technique. Accuracy of the method is analyzed in terms of the errors in \(L_2\) and \(L_\infty\). All of obtained results are discussed with an
example of the Burgers’ equation including numerical solutions for different situations of the fractional order and the behavior
of potentials u is investigated with graphically. All the obtained numerical results in this study are presented in tables. We used
the Mathematica software package in performing this numerical study.
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ISRP Style
Asıf Yokuş, Doğan Kaya, Numerical and exact solutions for time fractional Burgers' equation, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3419--3428
AMA Style
Yokuş Asıf, Kaya Doğan, Numerical and exact solutions for time fractional Burgers' equation. J. Nonlinear Sci. Appl. (2017); 10(7):3419--3428
Chicago/Turabian Style
Yokuş, Asıf, Kaya, Doğan. "Numerical and exact solutions for time fractional Burgers' equation." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3419--3428
Keywords
- Nonlinear time fractional Burgers’ equation
- an expansion method
- finite difference method
- Caputo formula
- linear stability
- Cole-Hopf transformation.
MSC
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