Derivation of explicit difference schemes for ordinary differential
Numerical methods and programming, Tome 11 (2010) no. 2, pp. 198-209
Voir la notice de l'article provenant de la source Math-Net.Ru
Some explicit multistage Runge-Kutta type methods for solving ordinary
differential equations (ODEs) are derived with the aid of the expansion of grid
functions in the Lagrange-Burmann series. The formulas are given
for the first four coefficients of the Lagrange-Burmann expansion. New explicit
first- and second-order methods are derived and applied to
the numerical integration of the Cauchy problem for a moderately
stiff ODE system. It turns out that the $L_2$-norm of the error
in the solution obtained by the new numerical second-order method
is 50 times smaller than that of the classical second-order
Runge-Kutta method.
Keywords:
ordinary differential equations; Lagrange-Burmann expansion; Runge-Kutta methods; stiff systems.
@article{VMP_2010_11_2_a6,
author = {E. V. Vorozhtsov},
title = {Derivation of explicit difference schemes for ordinary differential},
journal = {Numerical methods and programming},
pages = {198--209},
publisher = {mathdoc},
volume = {11},
number = {2},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMP_2010_11_2_a6/}
}
E. V. Vorozhtsov. Derivation of explicit difference schemes for ordinary differential. Numerical methods and programming, Tome 11 (2010) no. 2, pp. 198-209. http://geodesic.mathdoc.fr/item/VMP_2010_11_2_a6/