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Numerical methods for the two-dimensional multi-term time-fractional diffusion equations

机译:二维多维时间分形扩散方程的数值方法

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In this paper, we consider a numerical approach based on the matrix transfer method for numerical solution of multi-term time-fractional diffusion equations (MT-TFDEs). The semi- and fully-discrete schemes are developed by using the classical finite difference method and the matrix transfer technique. The unconditional stability and convergence of these two schemes are discussed and theoretically proved. The technique is then extended to MT-TFDEs with fractional Laplace operator. Numerical examples are given to validate and investigate the efficiency and the accuracy of the developed schemes. The results indicate that the present schemes are very effective for modeling and simulation of the MT-TFDEs with integral or fractional Laplacians. (C) 2017 Elsevier Ltd. All rights reserved.
机译:在本文中,我们考虑一种基于矩阵传递法的数值方法,用于求解多项式时间分数阶扩散方程(MT-TFDE)的数值解。通过使用经典的有限差分法和矩阵传递技术来开发半离散和全离散方案。讨论并从理论上证明了这两种方案的无条件稳定性和收敛性。然后,该技术通过分数Laplace运算符扩展到MT-TFDE。数值算例验证和研究了所开发方案的效率和准确性。结果表明,该方案对于带有积分或分数拉普拉斯算子的MT-TFDE的建模和仿真非常有效。 (C)2017 Elsevier Ltd.保留所有权利。

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