A linearization‐based approach of homotopy analysis method for non‐linear time‐fractional parabolic PDEs. (16th August 2019)

• Record Type: Journal Article
• Authors: Odibat, Zaid; Baleanu, Dumitru
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 18(2020)
• Page Start: 7222
• Page End: 7232
• Publication Date: 2019-08-16
• Subjects: homotopy analysis method -- linearization‐based approach of HAM -- series solution -- time‐fractional parabolic PDE; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5829
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.