【摘要】 求解一个常微分方程初值问题y’=f（x，y），y（xo）=y0的数值方法可分为两类。其中一类是一步法，目前提高一步法的价数都是通过使用高阶导教来实现的，比如要得到一个四阶一步法，在其计算公式中就需使用函数f（X，y）的直到三阶的偏导数，才能保证方法为四阶方法。由于一般情况下求f（X，y）的高阶导数都是相当麻烦的，这就使得高阶一步法在实际应用中受到很大程度的限制。本文给出了一个不需使用f（x，y）的高阶导数的四阶一步法，克服了通过使用高阶导数提高一步法阶数的缺陷。更多还原

【Abstract】 Chlculation of numrical solution on the initial value problem y’ = f(x, y ), y (xo ) =yo of first order ordinary differential equations has two mehch. One of them is the single step rule . It is by using higher derivative that the orde of single step rule has been increased up to now. For example, in ordr to use the fourth ordr single step rule, the upto third order partial derivative on funtion f(x, y) mus be ued. The use of higher other single step rule is restricted in a high degree in application because, in general, there are many difficulties in the process of solving higher derivative. This paper works out a fourth order singe step rule which, is used without soving higher dervtive on function f(x, y), so that the weakness of using higher derivaive in the fourth orde single rule is surmounted.更多还原