Hu, Min (1993) On variable coefficient multistep methods. Doctoral (PhD) thesis, Memorial University of Newfoundland.
- Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
In this monograph, we develop a subclass of variable coefficient multistep (VCM) methods, which is A-contractive. -- We introduce a set of simplifying conditions to relate VCM methods to the Padé approximants of the exponential function exp(z). We then proceed with the construction of the arbitrary order, A-contractive, variable stepsize VCM methods. Both linearly implicit and fully implicit families are considered. -- The convergence properties of VCM methods are discussed in chapter 3. We show the stiff-independent convergence for VCM methods on general nonlinear dissipative problems. We also demonstrate convergence of VCM methods when applied to singular perturbation problems with the convergence being independent of the perturbation parameter. -- Finally, in chapter 4 we report on a set of numerical experiments with fourth and fifth order linearly implicit and fully implicit methods.
|Item Type:||Thesis (Doctoral (PhD))|
|Additional Information:||Bibliography: leaves 115-118.|
|Department(s):||Science, Faculty of > Mathematics and Statistics|
|Library of Congress Subject Heading:||Stiff computation (Differential equations); Differential equations--Numerical solutions; Padé approximant|
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