Explicit two-step Runge-Kutta methods

Jackiewicz, Zdzisław, Renaut, Rosemary Anne, and Zennaro, Marino. "Explicit two-step Runge-Kutta methods." Applications of Mathematics 40.6 (1995): 433-456. <http://eudml.org/doc/32931>.

@article{Jackiewicz1995,
abstract = {The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order $p\le 5$ the minimal number of stages for explicit TSRK method of order $p$ is equal to the minimal number of stages for explicit Runge-Kutta method of order $p-1$. Numerical results are presented which demonstrate that constant step size TSRK can be both effectively and efficiently used in an Euler equation solver. Furthermore, a comparison with a variable step size formulation shows that in these solvers the variable step size formulation offers no advantages compared to the constant step size implementation.},
author = {Jackiewicz, Zdzisław, Renaut, Rosemary Anne, Zennaro, Marino},
journal = {Applications of Mathematics},
keywords = {explicit two-step Runge-Kutta methods; 4-stage order 5 method; numerical tests},
language = {eng},
number = {6},
pages = {433-456},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Explicit two-step Runge-Kutta methods},
url = {http://eudml.org/doc/32931},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Jackiewicz, Zdzisław
AU - Renaut, Rosemary Anne
AU - Zennaro, Marino
TI - Explicit two-step Runge-Kutta methods
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 6
SP - 433
EP - 456
AB - The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order $p\le 5$ the minimal number of stages for explicit TSRK method of order $p$ is equal to the minimal number of stages for explicit Runge-Kutta method of order $p-1$. Numerical results are presented which demonstrate that constant step size TSRK can be both effectively and efficiently used in an Euler equation solver. Furthermore, a comparison with a variable step size formulation shows that in these solvers the variable step size formulation offers no advantages compared to the constant step size implementation.
LA - eng
KW - explicit two-step Runge-Kutta methods; 4-stage order 5 method; numerical tests
UR - http://eudml.org/doc/32931
ER -