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A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs
Author(s) -
Odibat Zaid,
Baleanu Dumitru
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5829
Subject(s) - homotopy analysis method , mathematics , linearization , homotopy , homotopy perturbation method , series (stratigraphy) , mathematical optimization , nonlinear system , mathematical analysis , pure mathematics , paleontology , physics , quantum mechanics , biology
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.