中文摘要：

Butler-Volmer方程是电化学系统中描述电极动力学过程的本构方程，具有强非线性．为了对这一方程（耦合两个Ohm方程）进行解析求解，在同伦分析方法的框架下，发展了满足简单条件的广义非线性算子的算法，以取代原同伦分析中的非线性算子．该广义非线性算子的构造保证了高阶形变方程的线性特征．这一方法的有效性通过一些算例得到了验证．最后通过同伦分析方法对Butler-Volmer方程进行了求解，结果显示过电位和电流密度的级数解析解与数值解吻合很好，并有很好的收敛效率。

英文摘要：

Butler-Volmer equation is the constitutive equation to describe the dynamic process of electrode reaction in electrochemical systems. Due to its strong nonlinearity in the mathe- matical form, the computing efficiency by numerical methods was frequently limited. Aiming at solving this equation （ coupled with two Ohm equations） more efficiently, an improved homotopy analysis method（HAM） was presented, in which a generalized nonlinear operator satisfying simple conditions was developed to replace the nonlinear operator in the original homotopy. The construction of generalized nonlinear operator guaranteed the linear property of higher-order deformation equations. The validity of this method was verified through some examples. Furthermore, this method was successfully applied in solving Butler-Volmer equation. The analytical solutions of overpotential and current density agree very well with the numerical solutions and the high efficiency is shown in the computing process.