International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 31, Pages 1947-1959

Gaussian quadrature rules and A-stability of Galerkin schemes for ODE

Ali Bensebah,1 François Dubeau,2 and Jacques Gélinas3

1Commission Scolaire de Montréal (CSDM), 3737 rue Sherbrooke Est, Montréal HIX 3B3, Quebec, Canada
2Département de Mathématiques et d'Informatique, Faculté des Sciences, Université de Sherbrooke, 2500 boulevard Université, Sherbrooke J1K 2R1, Quebec, Canada
3Defence Research and Development Canada-Ottawa, 3701 Carling Avenue, Ottawa K1A 0Z4, Ontario, Canada

Received 20 November 2002

Copyright © 2003 Ali Bensebah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The A-stability properties of continuous and discontinuous Galerkin methods for solving ordinary differential equations (ODEs) are established using properties of Legendre polynomials and Gaussian quadrature rules. The influence on the A-stability of the numerical integration using Gaussian quadrature rules involving a parameter is analyzed.