Error Control Of Initial Value Problems For Stiff Ordinary Differential Equations Using Neumaier’s Method:-Obilo, Charles Ihinwanne .M.
ABSTRACT
Compared with standard numerical methods for
initial value problems (IVPs) for ordinary differential equations (ODEs), validated
methods not only compute a numerical solution to aproblem, 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 for IVPs over the past few decades. However, none of the validated
methods develop to date are suitable for stiff problems. This thesis
investigates the potential of Neumaier’s validated method for solving stiff
IVPs for ODEs. We show that Neumaier’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 p there is no
wrapping effect.
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CHARLES, M (2023). Error Control Of Initial Value Problems For Stiff Ordinary Differential Equations Using Neumaier’s Method:-Obilo, Charles Ihinwanne .M.. Repository.mouau.edu.ng: Retrieved May 11, 2024, from https://repository.mouau.edu.ng/work/view/error-control-of-initial-value-problems-for-stiff-ordinary-differential-equations-using-neumaiers-method-obilo-charles-ihinwanne-m-7-2
MACDONALD, CHARLES. "Error Control Of Initial Value Problems For Stiff Ordinary Differential Equations Using Neumaier’s Method:-Obilo, Charles Ihinwanne .M." Repository.mouau.edu.ng. Repository.mouau.edu.ng, 19 Oct. 2023, https://repository.mouau.edu.ng/work/view/error-control-of-initial-value-problems-for-stiff-ordinary-differential-equations-using-neumaiers-method-obilo-charles-ihinwanne-m-7-2. Accessed 11 May. 2024.
MACDONALD, CHARLES. "Error Control Of Initial Value Problems For Stiff Ordinary Differential Equations Using Neumaier’s Method:-Obilo, Charles Ihinwanne .M.". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 19 Oct. 2023. Web. 11 May. 2024. < https://repository.mouau.edu.ng/work/view/error-control-of-initial-value-problems-for-stiff-ordinary-differential-equations-using-neumaiers-method-obilo-charles-ihinwanne-m-7-2 >.
MACDONALD, CHARLES. "Error Control Of Initial Value Problems For Stiff Ordinary Differential Equations Using Neumaier’s Method:-Obilo, Charles Ihinwanne .M." Repository.mouau.edu.ng (2023). Accessed 11 May. 2024. https://repository.mouau.edu.ng/work/view/error-control-of-initial-value-problems-for-stiff-ordinary-differential-equations-using-neumaiers-method-obilo-charles-ihinwanne-m-7-2