caa a22 4500 465751857 CHVBK 20180323111836.0 cr unu---uuuuu 170327e19900901xx s 000 0 eng 10.1007/BF02242920 doi (NATIONALLICENCE)springer-10.1007/BF02242920 Runge-Kutta interpolants based on values from two successive integration steps [Elektronische Daten] [Ch. Tsitouras, G. Papageorgiou] Runge-Kutta Interpolanten gestützt auf Werte von zwei sukzessiven Integrationsschritten New interpolants of the explicit Runge-Kutta method for the initial value problem are proposed. These interpolants are based on values of the solution and its derivative from two successive integration steps. In this paper, three interpolants withO(h 6) local error (l.e.), for the fifth order solution, of the methods Fehlberg 4(5) (RKF 4(5)), Dormand and Prince 5(4) (RKDP 5(4)) and Verner 5(6) (RKV 5(6)) without extra cost are derived. An interpolant withO(h 7) (l.e.) for the sixth order solution of the Verner's method with only one extra function evaluation per integration step is also constructed. The above advantages are obtained without any cost in the magnitude of the error. Springer-Verlag, 1990 65L05 nationallicence Initial value problem nationallicence Rung-Kutta methods nationallicence Interpolation nationallicence Tsitouras Ch Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 73, Athens, Greece aut Papageorgiou G. Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 73, Athens, Greece aut Computing Springer-Verlag 43/3(1990-09-01), 255-266 0010-485X 43:3<255 1990 43 607 https://doi.org/10.1007/BF02242920 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02242920 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Tsitouras Ch Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 73, Athens, Greece aut NATIONALLICENCE 700 1- Papageorgiou G. Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 73, Athens, Greece aut NATIONALLICENCE 773 0- Computing Springer-Verlag 43/3(1990-09-01), 255-266 0010-485X 43:3<255 1990 43 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer