Five 4-dimensional families of embedded (4, 5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property (a_7j = b_j, 1 <= j <= 7, c_7 = 1) are derived. Previously known pairs satisfy simplifying assumption sum_j a_ij c_j = c_i^2 / 2, i >= 3, and constitute two of these families. Three families consist of non-FSAL pairs of 6-stage methods, as the 7th stage is not used.

翻译：包含FSAL财产(a_7j = b_j, 1 ⁇ j = 7, c_7 = 1)的5个四维的嵌入式(4, 5)对7级长式龙格-库塔法(a_7j = 7, c_7 = 1)的直立7级龙格-库塔法(a_7j = j j = 7, c_7 = 1)是衍生出来的。以前已知的对子符合简化的假设 sum_j a_ij c_j = c_2, i_2, i i = 2, i = 3 i i 3, 构成其中的2个家庭。三个家庭由非FSAL的6级方法组成,因为第7级没有使用。