Finite Difference and Sinc-Collocation Approximations to a Class of Fractional Diffusion-Wave Equations
Finite Difference and Sinc-Collocation Approximations to a Class of Fractional Diffusion-Wave Equations
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DOI：
10.1155/2014/536030
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发表时间：
2014-07
期刊：
影响因子：
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通讯作者：
Zhi Mao;A. Xiao;Zu-Guo Yu;Long Shi
中科院分区：
文献类型：
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作者：
Zhi Mao;A. Xiao;Zu-Guo Yu;Long Shi
针对一类具有Caputo分数阶导数的分数阶扩散波方程提出了一种有效的数值方法。这种方法是基于时间上的有限差分和空间上的全局sinc配置。利用配置技术和sinc函数的一些性质，问题归结为在每个时间步的线性代数方程组的解决方案。所提出的方法的稳定性和收敛性进行了严格的分析。数值解在时间上具有阶精度，在空间上具有指数收敛速度。数值实验验证了方法的有效性，支持了理论结果.
We propose an efficient numerical method for a class of fractional diffusion-wave equations with the Caputo fractional derivative of order . This approach is based on the finite difference in time and the global sinc collocation in space. By utilizing the collocation technique and some properties of the sinc functions, the problem is reduced to the solution of a system of linear algebraic equations at each time step. Stability and convergence of the proposed method are rigorously analyzed. The numerical solution is of order accuracy in time and exponential rate of convergence in space. Numerical experiments demonstrate the validity of the obtained method and support the obtained theoretical results.