<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Lubuma, Jean M-S</style></author><author><style face="normal" font="default" size="100%">Roux, Alet</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An Improved Theta-method for Systems of Ordinary Differential Equations</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Difference Equations and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Mathematical Finance</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1080/1023619031000146904</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">9</style></volume><pages><style face="normal" font="default" size="100%">1023-1035</style></pages><isbn><style face="normal" font="default" size="100%">1023-6198</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">The $\theta$-method of order $1$ or $2$ (if $\theta=1/2$) is often used for the numerical solution of systems of ordinary differential equations. In the particular case of linear constant coefficient stiff systems the constraint $1/2\le\theta\le1$, which excludes the explicit forward Euler method, is essential for the method to be $A$-stable. Moreover, unless $\theta=1/2$, this method is not elementary stable in the sense that its fixed-points do not display the linear stability properties of the fixed-points of the involved differential equation. We design a non-standard version of the $\theta$-method of the same order. We prove a result on the elementary stability of the new method, irrespective of the value of the parameter $\theta\in[0,1]$. Some absolute elementary stability properties pertinent to stiffness are discussed.</style></abstract><custom2><style face="normal" font="default" size="100%">MR2027165</style></custom2></record></records></xml>