A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs
A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs
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DOI：
10.1002/mma.5829
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发表时间：
2019-08
影响因子：
2.9
通讯作者：
Z. Odibat;D. Baleanu
中科院分区：
文献类型：
--
作者：
Z. Odibat;D. Baleanu
本文提出了一种新的方法，即基于线性化的同伦分析方法，来解析处理非线性时间分数阶偏微分方程。所提出的方法提出了一种新的优化结构的同伦级数解决方案的基础上的非线性问题的线性近似。通过求解两个非线性时间分数阶抛物型偏微分方程的算例，对所提出的方法和标准同伦分析方法进行了比较研究.数值模拟结果表明，基于线性化的方法降低了同伦分析方法的计算复杂度，提高了同伦分析方法的性能.
In this paper, a novel approach, namely, the linearization‐based approach of homotopy analysis method, to analytically treat non‐linear time‐fractional PDEs is proposed. The presented approach suggests a new optimized structure of the homotopy series solution based on a linear approximation of the non‐linear problem. A comparative study between the proposed approach and standard homotopy analysis approach is illustrated by solving two examples involving non‐linear time‐fractional parabolic PDEs. The performed numerical simulations demonstrate that the linearization‐based approach reduces the computational complexity and improves the performance of the homotopy analysis method.