Fractional integration operator for numerical solution of the integro-partial time fractional diffusion heat equation with weakly singular kernel
Fractional integration operator for numerical solution of the integro-partial time fractional diffusion heat equation with weakly singular kernel
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DOI：
10.1142/s1793557117500711
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发表时间：
2017-10
影响因子：
0.8
通讯作者：
Sedigheh Zaeri;H. Saeedi;M. Izadi
中科院分区：
文献类型：
--
作者：
Sedigheh Zaeri;H. Saeedi;M. Izadi
给出了时间分数阶弱奇异核偏积分-微分方程解的一个近似解。该方法基于二阶时间差分近似，然后应用分数次积分算子和分段线性插值法计算离散化过程中出现的核的奇异性。在von Neumann分析意义下，还考虑了该方法的稳定性。数值算例验证了该方法的有效性和适用性。
In this paper, an approximate solution for solving weakly singular kernel partial integro-differential equations with time fractional order is proposed. The method is based on using a second-order time difference approximation followed by applying the fractional integral operator and piecewise linear interpolation to compute the singularity of the kernel that appear in the discretization process. The stability of the method is also considered in the sense of von Neumann analysis. Numerical examples are solved to demonstrate the validity and applicability of the presented technique.