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Home  >  Volume 25 (2013)

Error Control of Initial Value Problems for Stiff Ordinary Differential Equations Using Neumaier’s Method by George N. Emenogu. Volme 25 ( Nov. 2013). pp 51-54
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Validated methods when compared with standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODES) not only compute a numerical solution to a problem, but also generate guaranteed global error bounds associated with the numerical solution.  There have been significant developments in the field of validated numerical methods for IVPs over the past few decades.  However, none of the validated methods develop to date are suitable for stiff problems.  This paper investigated the potential of Neumaier’s validated methods for solving stiff IVPs for ODES.  Neumaier’s result which is a special case of Dahlquist’s [1] result shows from our findings an effective validated method for stiff IVPs for ODES, for problems where there is no wrapping effect.