Validated Numerical Bounds on the Global Error for Initial Value Problems for Stiff Ordinary Differential Equations

Validated Numerical Bounds on the Global Error for Initial Value Problems for Stiff Ordinary Differential Equations Chao Yu Master of Science Graduate Department of Computer Science University of Toronto 2004 There are many standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs). Compared with these methods, validated methods for IVPs for ODEs produce bounds that are guaranteed to contain the true solution of a problem, if the true solution exists and is unique. The main result of this thesis is a formula to bound the global error associated with the numerical solution of a stiff IVP for an ODE. We give the complete proof of this result. Moreover, we derive Dahlquist’s formula and Neumaier’s formula from this formula. We also give alternative (and possibly simpler) proofs of some known related results.