Neumaier’s Method for the Solution of Initial Value Problems for Stiff Ordinary Differential Equations

Neumaier’s Method For The Solution Of Initial Value Problems For Stiff Ordinary Differential Equations Annie Hsiao Chen Yuk Master of Science Graduate Department of Computer Science University of Toronto 2005 Compared with standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs), validated methods not only compute a numerical solution to a problem, but also generate a guaranteed bound on the global error associated with the numerical solution. There have been significant developments in the field of validated numerical methods of IVPs over the past few decades. However, none of the validated methods developed to date are suitable for stiff IVPs for ODEs. This thesis investigates the potential of Neumaier’s validated method for stiff IVPs for ODEs. We show that Neuamier’s result is a special case of Dahlquist’s result. Our findings show that this method has promise as an effective validated method for stiff IVPs for ODEs, for problems where there is no wrapping effect.