Explicit two-step Runge-Kutta methods
Applications of Mathematics, Tome 40 (1995) no. 6, pp. 433-456
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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.
@article{10_21136_AM_1995_134306,
author = {Jackiewicz, Zdzislaw and Renaut, Rosemary Anne and Zennaro, Marino},
title = {Explicit two-step {Runge-Kutta} methods},
journal = {Applications of Mathematics},
pages = {433--456},
publisher = {mathdoc},
volume = {40},
number = {6},
year = {1995},
doi = {10.21136/AM.1995.134306},
mrnumber = {1353972},
zbl = {0849.65055},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134306/}
}
TY - JOUR AU - Jackiewicz, Zdzislaw AU - Renaut, Rosemary Anne AU - Zennaro, Marino TI - Explicit two-step Runge-Kutta methods JO - Applications of Mathematics PY - 1995 SP - 433 EP - 456 VL - 40 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134306/ DO - 10.21136/AM.1995.134306 LA - en ID - 10_21136_AM_1995_134306 ER -
%0 Journal Article %A Jackiewicz, Zdzislaw %A Renaut, Rosemary Anne %A Zennaro, Marino %T Explicit two-step Runge-Kutta methods %J Applications of Mathematics %D 1995 %P 433-456 %V 40 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.21136/AM.1995.134306/ %R 10.21136/AM.1995.134306 %G en %F 10_21136_AM_1995_134306
Jackiewicz, Zdzislaw; Renaut, Rosemary Anne; Zennaro, Marino. Explicit two-step Runge-Kutta methods. Applications of Mathematics, Tome 40 (1995) no. 6, pp. 433-456. doi: 10.21136/AM.1995.134306
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