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Numerical and exact solutions for time fractional Burgers' equation
- Source :
- The Journal of Nonlinear Sciences and Applications. 10:3419-3428
- Publication Year :
- 2017
- Publisher :
- International Scientific Research Publications MY SDN. BHD., 2017.
-
Abstract
- WOS: 000409101400006 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-infinity. 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. (C) 2017 All rights reserved.
- Subjects :
- Algebra and Number Theory
Mathematical analysis
01 natural sciences
010305 fluids & plasmas
Burgers' equation
010101 applied mathematics
Caputo formula
an expansion method
0103 physical sciences
0101 mathematics
finite difference method
linear stability
Analysis
Nonlinear time fractional Burgers' equation
Cole-Hopf transformation
Mathematics
Subjects
Details
- ISSN :
- 20081901 and 20081898
- Volume :
- 10
- Database :
- OpenAIRE
- Journal :
- The Journal of Nonlinear Sciences and Applications
- Accession number :
- edsair.doi.dedup.....ad56c7cf48f1e186ce3abf032bdf1970