A note concerning Gauss-Jackson method.

González, Ana B., and Martín, Pablo. "A note concerning Gauss-Jackson method.." Extracta Mathematicae 11.2 (1996): 255-260. <http://eudml.org/doc/38466>.

@article{González1996,
abstract = {Specialized literature concerning studies on Orbital Dynamics usually mentions the Gauss-Jackson or sum squared (∑2) method for the numerical integration of second order differential equations. However, as far as we know, no detailed description of this code is available and there is some confusion about the order of the method and its relation with the Störmer method. In this paper we present a simple way of deriving this algorithm and its corresponding analog for first order equations from the Störmer and Adams methods respectively. We show that the Gauss-Jackson method can be conceived as a consequence of this, and therefore there is no difficulty in determining the order of the method. Finally, we obtain an initialization technique for its implementation, we show an advantage of it as compared with the traditional multistep methods when applied in PEC mode by supressing the corrector stage in the intermediate steps.},
author = {González, Ana B., Martín, Pablo},
journal = {Extracta Mathematicae},
keywords = {Ecuaciones diferenciales; Ecuaciones de segundo orden; Integración numérica; Mecánica celeste; multistep method; Gauss-Jackson method; Cauchy problem; order},
language = {eng},
number = {2},
pages = {255-260},
title = {A note concerning Gauss-Jackson method.},
url = {http://eudml.org/doc/38466},
volume = {11},
year = {1996},
}

TY - JOUR
AU - González, Ana B.
AU - Martín, Pablo
TI - A note concerning Gauss-Jackson method.
JO - Extracta Mathematicae
PY - 1996
VL - 11
IS - 2
SP - 255
EP - 260
AB - Specialized literature concerning studies on Orbital Dynamics usually mentions the Gauss-Jackson or sum squared (∑2) method for the numerical integration of second order differential equations. However, as far as we know, no detailed description of this code is available and there is some confusion about the order of the method and its relation with the Störmer method. In this paper we present a simple way of deriving this algorithm and its corresponding analog for first order equations from the Störmer and Adams methods respectively. We show that the Gauss-Jackson method can be conceived as a consequence of this, and therefore there is no difficulty in determining the order of the method. Finally, we obtain an initialization technique for its implementation, we show an advantage of it as compared with the traditional multistep methods when applied in PEC mode by supressing the corrector stage in the intermediate steps.
LA - eng
KW - Ecuaciones diferenciales; Ecuaciones de segundo orden; Integración numérica; Mecánica celeste; multistep method; Gauss-Jackson method; Cauchy problem; order
UR - http://eudml.org/doc/38466
ER -