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The general case of embedded (4, 5) pairs of explicit 7-stage Runge--Kuttamethods 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. Thepairs within two (already known) families satisfy the simplifying assumptionsum_j a_ij c_j = c_i^2 / 2, i >= 3.

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