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

作者：Odibat Zaid^*; Bataineh A Sami

来源：Mathematical Methods in the Applied Sciences, 2015, 38(5): 991-1000.

DOI：10.1002/mma.3136

• homotopy analysis method
• homotopy polynomials
• Taylor series
• nonlinear differential equation
• the quadratic Riccati equation
• the pendulum equation

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.

• 出版日期2015-3-30