Embedded (4, 5) pairs of explicit 7-stage Runge-Kutta methods with FSAL property

Abstract

The general case 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) is considered. Besides exceptional cases, the pairs form five 4-dimensional families. The pairs within two (already known) families satisfy the simplifying assumption sum_j a_ij c_j = c_i^2 / 2, i >= 3.

arXiv comment18 pages, 3 figures, 7 tables. New version adds citation to (Tsitouras, 2011) paper, pair in Table 4 is changed, more numerical tests are added