In order to understand the two types of nonlinear differential equation problems in engineering dynamics, the author proposes a numerical analysis method for the two types of nonlinear differential equations based on computer simulation. This method establishes the MATLAB algorithm structure of the numerical solution of the fourth-order fixed-step Runge-Kutta and Lorenz models, discusses the error control in the case of variable step size, and plots the numerical solutions of the Lorenz system based on MATLAB in two-dimensional and three-dimensional space graphics. The x -direction displacement and y -direction displacement data are extracted from the Lorenz equation as iterative samples of the model, the regression curve obtained after iteration has a slope of 0.996, and the iterative regression model reflects the basic characteristics of the data well. This method presents the basic idea of numerical solution verification within acceptable error limits. For solving engineering problems with differential equations as mathematical models, an effective numerical solution method is provided, and further discussion on the numerical solutions of partial differential equations is of great significance.