International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 31, Pages 1947-1959
doi:10.1155/S0161171203211467
Gaussian quadrature rules and A-stability of Galerkin schemes for ODE
Ali Bensebah1
, François Dubeau2
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
Abstract
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.