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Essay On Homotopy Analysis

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Assignment of Research Methodology Student Name: Nisha Shukla Enrollment No.: 14408002 Department: Mathematics Topic: Review of thesis Thesis details Authors Name: Erik Sweet Topic of Thesis: Analytical and Numerical solutions of differential equations arising in fluid flow and Heat transfer University: University of Central Florida Orlando, Florida Year: 2009 1. Brief Summary of Thesis: In this thesis, Homotopy analysis method (HAM) has been applied to obtain the solutions of nonlinear differential equations arising in fluid flow and Heat transfer. This method …show more content…

There are many other analytical methods exist for solving nonlinear differential equations, for example: Adomin’s decomposition method, Homotopy perturbation method (HPM), Liapunov’s artificial method etc. But HAM is more general in comparison of all of these methods. In this thesis, author presents a difference between HPM and HAM, but he has not compared the results of any problem obtained by HAM and HPM. He presents only a theoretical description of comparison of methods. In HAM, we have to choose an initial guess, a linear operator and a convergence control parameter h. According to Liao, we can choose these parameters freely. This thesis provides a way to select an appropriate linear operator and value of convergence parameter. Non-uniqueness of linear operator has also mentioned, which shows the independency of choosing a linear operator. Author has applied HAM to solve a system of nonlinear partial and ordinary differential equations, which shows a significant application of HAM. But he has not solved any system of more than two equations; this is a drawback of this thesis. In chapter 3, some theorems are given to show the existence of solution. In fluid flow problems, many differential equations have multiple solutions, but in this thesis this case has not

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