SONG Hui, LI Fen, XU Xian-zhi. Analytical Solution of Butler-Volmer Equation in Battery System Modeling[J]. Applied Mathematics and Mechanics, 2013, 34(4): 373-382. doi: 10.3879/j.issn.1000-0887.2013.04.006
 Citation: SONG Hui, LI Fen, XU Xian-zhi. Analytical Solution of Butler-Volmer Equation in Battery System Modeling[J]. Applied Mathematics and Mechanics, 2013, 34(4): 373-382.

# Analytical Solution of Butler-Volmer Equation in Battery System Modeling

##### doi: 10.3879/j.issn.1000-0887.2013.04.006
• Rev Recd Date: 2013-04-03
• Publish Date: 2013-04-15
• 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 mathematical 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.
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