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Full-Text Articles in Mathematics
Numerical Methods (Finite Element) For Time-Dependent Partial Differential Equations, Masaji Watanabe
Numerical Methods (Finite Element) For Time-Dependent Partial Differential Equations, Masaji Watanabe
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This paper surveys reasons why the Ritz method and the Galerkin method are not efficient and why these methods can not be applied directly, for time dependent problems. It also introduces methods that are used for those problems. For a linear boundary value problem defined by a positive definite symmetric (self-adjoint) operator, the existence and the convergence of the Ritz approximation are guaranteed. In non-symmetric case, Lax-Milgram lemma assures the existence and the convergence of the Galerkin approximation for H1/2(Ω)-elliptic operator. Since time-dependent problems are hyperbolic or parabolic, the existence and the convergence of approximations by those methods are not …
The Shape Seeker Algorithm, Ladawn Haws
The Shape Seeker Algorithm, Ladawn Haws
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This paper gives a brief description of several well known fuzzy objective function clustering algorithms, and discusses the convergence properties of this type of algorithm. The Shape Seeker algorithm, an adaptive norm algorithm, is then described in detail, and convergence established. It is compared to the other algorithms by examining the clusterings it produces on several data sets.