将结构的位移及速度响应作为状态变量，采用Lyapunov（李雅普诺夫）人工小参数法求解状态方程，导出状态方程的一个新的级数形式的解析解，该解析解还可以推广到非线性动力方程的计算。将秦九韶算法引入级数解的计算，提高了计算的效率和稳定性，同时给出了本文算法的计算格式和步骤。该算法无需对转换矩阵H求逆，仅使用矩阵向量相乘，计算稳定，精度仅由收敛项数控制，很容易达到任意精度要求，而且适合并行计算及压缩存储。最后通过算例进一步证实了本文算法的精度和效率。

In this paper, the displacement and speed response of the structure as the state variable. In order to solve the state equation, the Lypaunov artificial small parameter method is used, and a new series form of analytical solution is presented. The series solution can also be used to solve nonlinear dynamics equations. Hornor's scheme is applied to the calculation of series solution, and the computation efficiency and stability are greatly increased. At the same time, the corresponding computation format and steps for linear dynamics equations are established. The algorithm need only repetitious matrix-vector multiplication without inversion of H matrix，so the computation stability is good. The precise is only controlled by the series convergence number, so the algorithm can easily reach arbitrary-order accuracy in theory, and fit for parallel calculating and compression storage. At last, a numerical example is given to demonstrate the validity and efficiency of the method.