Huťa, Anton, and Penjak, Vladimír. "A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order." Aplikace matematiky 29.6 (1984): 411-422. <http://eudml.org/doc/15375>.
@article{Huťa1984,
abstract = {The purpose of this article is to find the 7th order formulas with rational parameters. The formulas are of the 11th stage. If we compare the coefficients of the development $\sum ^\infty _\{i=1\} \frac\{h^i\}\{i!\} \frac\{d^\{i-1\}\}\{dx^\{i-1\}\} \mathbf \{f\}\left[x,\mathbf \{y\}(x)\right]$ up to $h^7$ with the development given by successive insertion into the formula $h.f_i(k_0,k_1,\ldots , k_\{i-1\})$ for $i=1,2,\ldots , 10$ and $k=\sum ^\{10\}_\{i=0\} p_i, k_i$ we obtain a system of 59 condition equations with 65 unknowns (except, the 1st one, all equations are nonlinear). As the solution of this system we get the parameters of the 7th order Runge-Kutta formulas as rational numbers.},
author = {Huťa, Anton, Penjak, Vladimír},
journal = {Aplikace matematiky},
keywords = {Runge-Kutta formulas; rational coefficients; systems; 7th order formulas; Runge-Kutta formulas; rational coefficients; systems; 7th order formulas},
language = {eng},
number = {6},
pages = {411-422},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order},
url = {http://eudml.org/doc/15375},
volume = {29},
year = {1984},
}
TY - JOUR
AU - Huťa, Anton
AU - Penjak, Vladimír
TI - A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 6
SP - 411
EP - 422
AB - The purpose of this article is to find the 7th order formulas with rational parameters. The formulas are of the 11th stage. If we compare the coefficients of the development $\sum ^\infty _{i=1} \frac{h^i}{i!} \frac{d^{i-1}}{dx^{i-1}} \mathbf {f}\left[x,\mathbf {y}(x)\right]$ up to $h^7$ with the development given by successive insertion into the formula $h.f_i(k_0,k_1,\ldots , k_{i-1})$ for $i=1,2,\ldots , 10$ and $k=\sum ^{10}_{i=0} p_i, k_i$ we obtain a system of 59 condition equations with 65 unknowns (except, the 1st one, all equations are nonlinear). As the solution of this system we get the parameters of the 7th order Runge-Kutta formulas as rational numbers.
LA - eng
KW - Runge-Kutta formulas; rational coefficients; systems; 7th order formulas; Runge-Kutta formulas; rational coefficients; systems; 7th order formulas
UR - http://eudml.org/doc/15375
ER -