一类分数阶扩散波动方程的辛-切比雪夫配置法
Sinc-Chebyshev collocation method for a class of fractional diffusion-wave equations.
作者信息
Mao Zhi, Xiao Aiguo, Yu Zuguo, Shi Long
机构信息
Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China ; Mathematics and Information Engineering Department, Tongren University, Tongren, Guizhou 554300, China.
Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan 411105, China.
出版信息
ScientificWorldJournal. 2014;2014:143983. doi: 10.1155/2014/143983. Epub 2014 Apr 1.
This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed.
本文致力于研究一类具有变系数的分数阶扩散波方程的数值解，其中分数阶导数采用Caputo意义下的定义。该方法基于配置技术，分别利用时间上的移位切比雪夫多项式和空间上的正弦函数。该问题被归结为一个线性代数方程组的求解。通过数值例子，对该过程进行了测试，并证实了所提方法的有效性。
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