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1	Numerical Methods in Reaction Rate Theory Frankcombe, Terry James Unknown Date (has links) Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to 780103 Chemical sciences master equation matrix methods EGME gas phase nonequilibrium kinetics spectral eigenvalues eigenvectors HONE ERS Nesbet WIPSP subspace projection relative accuracy precision MPFUN quadruple precision double precision Chebyshev Lanczos Arnoldi coal graphene carbon ab initio B3LYP gasification
2	Numerical Methods in Reaction Rate Theory Frankcombe, Terry James Unknown Date (has links) Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to 780103 Chemical sciences master equation matrix methods EGME gas phase nonequilibrium kinetics spectral eigenvalues eigenvectors HONE ERS Nesbet WIPSP subspace projection relative accuracy precision MPFUN quadruple precision double precision Chebyshev Lanczos Arnoldi coal graphene carbon ab initio B3LYP gasification
3	Numerical Methods in Reaction Rate Theory Frankcombe, Terry James Unknown Date (has links) Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to 780103 Chemical sciences master equation matrix methods EGME gas phase nonequilibrium kinetics spectral eigenvalues eigenvectors HONE ERS Nesbet WIPSP subspace projection relative accuracy precision MPFUN quadruple precision double precision Chebyshev Lanczos Arnoldi coal graphene carbon ab initio B3LYP gasification
4	Numerical Methods in Reaction Rate Theory Frankcombe, Terry James Unknown Date (has links) Numerical methods are often required to solve chemical problems, either to verify theoretical models or to access information that is not readily available experimentally. This thesis deals with both situations, though in differing levels of detail. A major component of this thesis is devoted to developing new methods to determine a full eigendecomposition of the matrices derived from "low temperature" unimolecular master equations. When transient behaviour is of interest achieving relative accuracy for more than just the eigenvector corresponding to the smallest eigenvalue is of central importance. Three new methods are presented. The first is based on a weighted implementation of subspace projection methods, in this case explored for the well-known Arnoldi method. This weighted inner product subspace projection methodology is demonstrated to 780103 Chemical sciences master equation matrix methods EGME gas phase nonequilibrium kinetics spectral eigenvalues eigenvectors HONE ERS Nesbet WIPSP subspace projection relative accuracy precision MPFUN quadruple precision double precision Chebyshev Lanczos Arnoldi coal graphene carbon ab initio B3LYP gasification

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