An Operational Matrix Method for Fractional Advection-Diffusion Equations With Variable Coefficients
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摘要: 研究带Caputo分数阶导数的变系数对流扩散方程的数值解法.基于Chebyshev cardinal函数,推导RiemannLiouville分数阶积分的一个有效算子矩阵,以之为基础,提出了变系数分数阶对流扩散方程的一种新的算子矩阵法.该方法将方程的求解转化成矩阵的代数运算,具有计算量小和易于编程等特点.给出数值算例并与一些现有的方法进行比较,结果表明该方法是收敛的且在计算精度上占有优势.
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关键词:
- 分数阶微积分 /
- Chebyshev cardinal函数 /
- 分数阶对流扩散方程 /
- 算子矩阵方法
Abstract: A numerical method for the Caputo-fractional advection-diffusion equations with variable coefficients was investigated. Based on Chebyshev cardinal functions, an effective operational matrix was derived for Riemann-Liouville fractional integral, and with it, a new operational matrix method was proposed for the fractional advection-diffusion equations with variable coefficients. This method reduces the equation to an algebraic system and is characterized by small computing cost and easy programming. The numerical results and the comparisons with some existing methods illustrate that it is convergent and possesses advantages in accuracy. -
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