Misha Stepanov | publications | Calcolo (2022)

M. Stepanov, Embedded (4, 5) pairs of explicit 7‑stage Runge–Kutta methods with FSAL property, Calcolo 59 (4) 41 (2022).

DOI: 10.1007/s10092-022-00486-1
arXiv: 2108.12590
PDF (1.99 MB)

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, c₇ = 1) is considered. Besides exceptional cases, the pairs form five 4‑dimensional families. The pairs within two (already known) families satisfy the simplifying assumption ∑_j a_ij c_j = c_i²/ 2, i ≥ 3.