By means of an integral expression of non - linear dynamics equation an explicit precise integration algorithm with four order accuracy and self - correct and self - starting to solve this equation is given . this method is adapted to solve the non - conservative system with multi - dof and strong nonlinear . the non - linear dynamic equations are divided into some blocks or groups 给出了求解非线性动力学方程的精细积分表达式，利用插值近似该方程的非线性项，得到一个具有四阶精度并且是单步显式、自起步、预测-校正的lagrange (或hermite )插值精细积分算法，适于强非线性、非保守系统。
