An improved theta-method for systems of ordinary differential equations

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JournalJournal of Difference Equations and Applications
DatePublished - 2003
Issue number11
Volume9
Number of pages13
Pages (from-to)1023-1035
Original languageEnglish

Abstract

The $-method of order $1$ or $2$ (if $1/2$) 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 $1/2letheta$, which excludes the explicit forward Euler method, is essential for the method to be $A$-stable. Moreover, unless $1/2$, 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 $-method of the same order. We prove a result on the elementary stability of the new method, irrespective of the value of the parameter $theta0,1]$. Some absolute elementary stability properties pertinent to stiffness are discussed.

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