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Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica
Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica
Dissertations
Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits …
2-Domination And Annihilation Numbers, Sean C. Patterson
2-Domination And Annihilation Numbers, Sean C. Patterson
Honors Theses
Using information provided by Ryan Pepper and Ermelinda DeLaVina in their paper On the 2-Domination number and Annihilation Number, I developed a new bound on the 2- domination number of trees. An original bound, γ2(G) ≤ (n+n1)/ 2 , had been shown by many other authors. Our goal was to generate a tighter bound in some cases and work towards generating a more general bound on the 2-domination number for all graphs. Throughout the span of this project I generated and proved the bound γ2(T ) ≤ …