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An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials
Author(s) -
Odibat Zaid,
Sami Bataineh A.
Publication year - 2014
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.3136
Subject(s) - homotopy analysis method , mathematics , nonlinear system , homotopy , series (stratigraphy) , n connected , algebra over a field , mathematical optimization , pure mathematics , paleontology , physics , quantum mechanics , biology
In this paper, a new adaption of homotopy analysis method is presented to handle nonlinear problems. The proposed approach is capable of reducing the size of calculations and easily overcome the difficulty arising in calculating complicated integrals. Furthermore, the homotopy polynomials that decompose the nonlinear term of the problem as a series of polynomials are introduced. Then, an algorithm of calculating such polynomials, which makes the solution procedure more straightforward and more effective, is constructed. Numerical examples are examined to highlight the significant features of the developed techniques. The algorithms described in this paper are expected to be further employed to solve nonlinear problems in mathematical physics. Copyright © 2014 John Wiley & Sons, Ltd.