The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are determined by constructing a recurrence relation. To deal with nonlinearity of the problems, the Fa\`{a} di Bruno's formula containing the partial ordinary Bell polynomials is applied within the differential transform to avoid computation of symbolic derivatives. The error estimation results are presented too. Four concrete problems are studied to show efficiency and reliability of the method. The obtained results are compared to other methods.

翻译：微分变换法被用于求解一类特定非线性微分代数方程的数值近似解。该方法基于泰勒定理，通过构建递推关系确定泰勒级数的系数。为处理问题的非线性特性，在微分变换中应用了包含偏常贝尔多项式的Faà di Bruno公式，以避免符号导数的计算。本文还给出了误差估计结果。通过研究四个具体问题展示了该方法的有效性和可靠性，并将所得结果与其他方法进行了比较。