Runge-Kutta法の打切り精度の判定基準について

概要

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For the purpose of giving the error estimating ability to the Runge-Kutta method that uses three, four or five function values, we try to optimize it from the standpoint of truncation error under a certain condition. In such cases, it is necessary for us to judge the accuracy of truncation error of the formula. Therefore, we investigate the relation between certain measures and the real accuracy of truncation error. In regard to the cases of the second and the third order method, the problem has already been taken up by R. L. Johnston ([2]) and the effectiveness of the criteria has been proved, while as for the case of the fourth order one, the same has been done by T. E. Hull and R. L. Johnston. ([3]) In this paper, it will be studied whether we can measure the accuracy of truncation error by the use of the criteria concerning to the Runge-Kutta method which has the accuracy between that of the fourth order method and that of the fifth order one, and which uses five functional values per a step.
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