B‐spline solution of fractional integro partial differential equation with a weakly singular kernel
B‐spline solution of fractional integro partial differential equation with a weakly singular kernel
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DOI：
10.1002/num.22153
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发表时间：
2017-09
影响因子：
3.9
通讯作者：
Saima Arshed
中科院分区：
文献类型：
--
作者：
Saima Arshed
本文的主要目的是求具有弱奇异核的分数阶积分偏微分方程的近似解。积分偏微分方程（IPDE）出现在粘弹性现象的研究中。分数阶IPDE采用三次B样条配点法。所开发的计划，用于寻找所考虑的问题的解决方案是基于有限差分法和配置法。Caputo分数阶导数用于α阶的时间分数阶导数，0 < α < 1。在时间和空间两个方向上离散给定的问题。时间离散采用后向欧拉公式。空间离散采用配置法。所提出的格式被证明是稳定的，并且关于时间是收敛的。检查近似解以检查所提出的方法的精度和有效性。© 2017 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq 33：1565-1581，2017
The main objective of the paper is to find the approximate solution of fractional integro partial differential equation with a weakly singular kernel. Integro partial differential equation (IPDE) appears in the study of viscoelastic phenomena. Cubic B‐spline collocation method is employed for fractional IPDE. The developed scheme for finding the solution of the considered problem is based on finite difference method and collocation method. Caputo fractional derivative is used for time fractional derivative of order α, 0 < α < 1 . The given problem is discretized in both time and space directions. Backward Euler formula is used for temporal discretization. Collocation method is used for spatial discretization. The developed scheme is proved to be stable and convergent with respect to time. Approximate solutions are examined to check the precision and effectiveness of the presented method.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1565–1581, 2017