但在生产实践与科学技术研究中所遇到的微分方程往往很复杂，在多数情况下不

However, the differential equations encountered in production practice and scientific and technological research are often very complex. In most cases, the analytical expression of the solution cannot be obtained. Even if the formal solution can be obtained, it is often not due to the large amount of calculation It is too practical, and it is not easy to find roots of higher-order algebraic equations, so it is not appropriate to calculate numerical solutions of differential equations by seeking analytical solutions. In fact, for the problem of solving the initial value of differential equations, only the approximate solution of the obtained solution at several points or the expression of the solution that is easy to calculate is generally required.

However, the differential equations encountered in production practice and scientific and technological research are often very complex, in most cases can not find the solution of the analytical expression, even if the form of the solution can be found, it is often because of the large amount of calculation is not very practical, and the high-second algebraic equation root is not easy, so it is not appropriate to use the method of analysis to calculate the numerical solution of differential equations. In fact, for the problem of the initial value of the solution differential equation, it is generally required to obtain only the approximate solution or easy-to-calculate expression of the solution at several points.

However, the differential equations encountered in production practice and scientific and technological research are often very complex. In most cases, the analytical expression of the solution cannot be obtained. Even if the formal solution can be obtained, it is often not practical due to the large amount of calculation, and it is not easy to find the roots of higher-order algebraic equations, so it is not appropriate to calculate the numerical solution of the differential equation with the analytical solution method. In fact, for the initial value problem of solving differential equation, only the approximate solution of the obtained solution at several points or the expression of the solution which is easy to calculate are generally required.<br>