Two continuous (4, 5) pairs of explicit 9-stage Runge-Kutta methods
arXiv:2202.08443
Abstract
An 11-dimensional family of embedded (4, 5) pairs of explicit 9-stage Runge-Kutta methods with an interpolant of order 5 is derived. Two optimized for efficiency pairs are presented.
18 pages, 9 figures, 4 tables. New version corrects data in Figure 7, tests A3 and D5: now the efficiency curves for (Verner, 2020, tab. 3) and Table 4 pairs show maximal error along the whole trajectory (in previous version they erroneously were showing just the error at t = 20)