# An Improved Theta-method for Systems of Ordinary Differential Equations

Research group:
 Title An Improved Theta-method for Systems of Ordinary Differential Equations Publication Type Journal Article Year of Publication 2003 Authors Lubuma JM-S, Roux A Journal Journal of Difference Equations and Applications Volume 9 Pagination 1023-1035 Abstract 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. URL http://dx.doi.org/10.1080/1023619031000146904 MathRev MR2027165