We report on a novel algorithm for controlling global error in a step-by-step (stepwise) sense, in the numerical solution of a scalar, autonomous, nonstiff or weakly stiff problem. The algorithm exploits the remainder term of a Taylor expansion of the solution. It requires the use of the DP853 triple to solve an auxiliary problem which, in turn, enables the remainder term to be determined. A quenching process then allows the solution generated by Euler's method to be controlled. We have achieved tolerances on the relative global error as strict as 1e-10.

翻译：我们报道了一种新的算法，用于逐步控制标量，自动，不僵硬或弱僵硬问题的数值解的全局误差。该算法利用了解的泰勒级数的余项，并需要使用DP853三阶算法来解决辅助问题，通过这种方法，可以确定余项大小。然后，平稳过程允许控制由欧拉方法生成的解。我们实现了相对全局误差为1e-10的容限。