An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials

• Published in: Mathematical methods in the applied sciences Vol. 38; no. 5; pp. 991 - 1000
• Main Authors: Odibat, Zaid, Sami Bataineh, A.
• Format: Journal Article
• Language: English
• Published: Freiburg Blackwell Publishing Ltd 30.03.2015; Wiley Subscription Services, Inc
• Subjects: Adaptation; Algorithms; Construction; Handles; homotopy analysis method; homotopy polynomials; Integrals; Mathematical analysis; Mathematical models; nonlinear differential equation; Nonlinearity; Polynomials; Taylor series; the pendulum equation; the quadratic Riccati equation
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.3136

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.