利用DP853三元组和泰勒余项的欧拉方法的逐步全局误差控制
Stepwise global error control in Euler's method using the DP853 triple and the Taylor remainder term
摘要：
我们报告了一种新的算法控制全局误差在一步一步（逐步）的意义上，在数值解的标量，自治，非刚性或弱刚性问题。该算法利用泰勒展开的解决方案的剩余项。它需要使用DP 853三元组来解决一个辅助问题，从而使剩余项得以确定。然后，淬火过程允许控制由欧拉方法生成的解。我们已经实现了相对全局误差的公差严格为1 e-10。
英文摘要：
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.
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