An Improved Theta-method for Systems of Ordinary Differential Equations

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

Department of Mathematics