TY - JOUR
T1 - Embedded (4, 5) pairs of explicit 7-stage Runge–Kutta methods with FSAL property
AU - Stepanov, Misha
N1 - Funding Information: The author is grateful to anonymous reviewers for helpful comments and suggestions. Publisher Copyright: © 2022, The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT).
PY - 2022/11
Y1 - 2022/11
N2 - The general case of embedded (4, 5) pairs of explicit 7-stage Runge–Kutta methods with FSAL property (a7j= bj, 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 ∑jaijcj=ci2/2, i≥ 3.
AB - The general case of embedded (4, 5) pairs of explicit 7-stage Runge–Kutta methods with FSAL property (a7j= bj, 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 ∑jaijcj=ci2/2, i≥ 3.
KW - Adaptive step size control
KW - Embedded pairs of Runge–Kutta methods
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U2 - 10.1007/s10092-022-00486-1
DO - 10.1007/s10092-022-00486-1
M3 - Article
SN - 0008-0624
VL - 59
JO - CALCOLO
JF - CALCOLO
IS - 4
M1 - 41
ER -