利用同伦分析方法，得到了该模型的近似解。
Using the homotopy analysis method, the approximation solution is obtained.
利用同伦分析方法，得到了该模型解的近似展开式。
Using the homotopy analysis method, the approximation of the solution for the model was obtained.
本文给出了几个应用实例，以说明“同伦分析方法”的有效性及巨大的潜力。
Examples are given in this paper to show the validity of this method.
阐述利用最新提出的同伦分析方法求解有正阻尼的强非线性振动方程，得到了该方程的六阶近似解析解。
In this paper, the sixth-order approximate analytical solutions of the strong nonlinear oscillation with positive damping are obtained by using newly developed homotopy analysis method.
应用“同伦分析方法”成功求解了科学和工程中众多类型的非线性问题，证实了其有效性和普遍适用性。
The homotopy analysis method has been successfully applied to a lots of different types of nonlinear problems in science and engineering so as to prove its general validity in a wide region of fields.
用同伦方法分析了可分解映射的零点存在性，并获得它对一类非线性特征值问题的应用。
Using homotopy methods, this paper gives an analysis on the existence of zeros of the decomposable mapping, and finds its application to a class of nonlinear eigenvalue problems.
结果表明，同伦分析法在求解高维非线性演化方程时，仍然是一种行之有效的方法。
The results indicate that the HAM is still valid for solving a class of higher dimensional evolution equations.
同时在分析了同伦参数正则化效应的基础上，提出一种两段同伦参数修正方法。
Considering the regularization effect of homotopy parameter, we adopt a two-step update scheme of homotopy parameter.
同时在分析了同伦参数正则化效应的基础上，提出一种两段同伦参数修正方法。
Considering the regularization effect of homotopy parameter, we adopt a two-step update scheme of homotopy parameter.
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