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An Improved Method for the Construction of Nonlinear Operator in Homotopy Analysis Method



Nonliear equations containing strongly nonlinear items of the form of composition of unknown functions, such as and , are difficult to solve directly using analytical methods. An improved Homotopy Analysis Method(HAM) is presented in this paper to solve such kind of nonlinear equations, in which a generalized nonlinear operator satisfying simple conditions is developed to replace the nonlinear operator in the original homotopy. The linearity of high-order deformation equation is guaranteed by the generalized nonlinear operator contained in the zerothorder deformation equation so it is solvable and its solution still obey the solution expression. The original nonlinear operator becomes just a special case of the generalized nonlinear operator. The validity of this method is verified through some examples. The proposal of generalized nonlinear operator illustrates the great freedom on constructing the zeroth-order deformation equation in the framework of HAM

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