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2012•AIP conference proceedingsRequires access

A study of the initial guess in Homotopy analysis method

Li Zou, Wang Zhen, Zong Zhi, Tian Shoufu

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Abstract

In this paper, we study on the initial guess in homotopy analysis method. To illustrate our point, we applied to homotopy analysis method to solving the (2+1)dimensional boussinesq equation and (3+1) dimensional KP equation. Comparisons are made between the exact solution and the approximation of homotopy analysis method. Both of the analytic solutions agree well with the exact solutions. The results show that homotopy analysis method is a potential analytic method in solving nonlinear problems.

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What this paper is about

In this paper, we study on the initial guess in homotopy analysis method. To illustrate our point, we applied to homotopy analysis method to solving the (2+1)dimensional boussinesq equation and (3+1) dimensional KP equation. Comparisons are made between the exact solution and the approximation of homotopy analysis method. Both of the analytic solutions agree well with the exact solutions. The results show that homotopy analysis method is a potential analytic method in solving nonlinear problems.

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Available abstract

In this paper, we study on the initial guess in homotopy analysis method. To illustrate our point, we applied to homotopy analysis method to solving the (2+1)dimensional boussinesq equation and (3+1) dimensional KP equation. Comparisons are made between the exact solution and the approximation of homotopy analysis method. Both of the analytic solutions agree well with the exact solutions. The results show that homotopy analysis method is a potential analytic method in solving nonlinear problems.

Key concepts: Homotopy analysis method, Homotopy, Homotopy perturbation method, Mathematics, Nonlinear system, Point (geometry), Applied mathematics, Exact solutions in general relativity

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