Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix.
Numerical solution of the one-dimensional fractional convection diffusion equations based on Chebyshev operational matrix.
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DOI：
10.1186/s40064-016-2832-y
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Yang X
中科院分区：
文献类型：
--
作者：
Xie J;Huang Q;Yang X
本文研究了一维非线性分数阶对流扩散方程。构造了一种基于切比雪夫运算矩阵的变系数分数阶对流扩散方程的数值求解方法。该方法的主要特点是在分数阶微积分中构造了基于切比雪夫多项式的新的正交函数。推导了相应的分数阶差分运算矩阵。然后利用Tau方法得到的矩阵将该问题的解转化为线性代数方程组的求解。通过求解线性代数方程，得到了数值解。通过实例验证了该方法的有效性。实验结果表明，该算法具有较好的效果。误差分析表明，该算法是收敛的。
In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.