An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials. (10th April 2014)

• Record Type: Journal Article
• Authors: Odibat, Zaid; Sami Bataineh, A.
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 5(2015:Mar. 30)
• Page Start: 991
• Page End: 1000
• Publication Date: 2014-04-10
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3136
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma3136-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma3136-para-0001">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 &amp; Sons, Ltd.</p> </abstract>