Numerical and exact solutions for time fractional Burgers' equation
Numerical and exact solutions for time fractional Burgers' equation
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DOI：
10.22436/jnsa.010.07.06
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发表时间：
2017-07
期刊：
影响因子：
--
通讯作者：
A. Yokuş;D. Kaya
中科院分区：
文献类型：
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作者：
A. Yokuş;D. Kaya
利用展开法和Cole-Hopf变换求出了一类非线性时间分数阶Burgers方程的行波方程的精确解。为此，本文研究了一类具有初始条件的非线性时间分数阶Burgers方程.采用基于Caputo公式的有限差分法，并引入分数阶微分。利用ColeHopf变换将Burgers方程线性化，保证了FDM的稳定性。结果表明，采用傅立叶-冯诺依曼技术的有限差分法是稳定的。从L2和L∞误差的角度分析了该方法的精度。以Burgers方程为例讨论了所得结果，包括分数阶不同情况下的数值解，并用图解法研究了势u的行为。本研究中获得的所有数值结果均以表格形式呈现。我们使用的Mathematica软件包在执行这个数值研究。©2017版权所有。
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 ColeHopf 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 L2 and L∞. 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.