Numerical and exact solutions for time fractional Burgers' equation
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Tarih
2017
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Int Scientific Research Publications
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Nonlinear time fractional Burgers' equation, an expansion method, finite difference method, Caputo formula, linear stability, Cole-Hopf transformation
Kaynak
Journal of Nonlinear Sciences and Applications
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
10
Sayı
7
