Browsing by Subject "Boundary value problems"
Now showing 1 - 20 of 23
Results Per Page
Sort Options
Item A modified simple shooting method for solving two-point boundary value problems(Texas Tech University, 2003-05) Holsapple, Raymond W.In physics and engineering, one often encounters what is called a two-point boundary value problem (TPBVP). Several methods exist, for solving these problems. Shooting methods, such as the Simple Shooting Method (SSM) and its variation, the Multiple Shooting Method (MSM) are two popular methods used to solve TPBVPs. In this thesis, a new method is proposed that was designed from the favorable aspects of both the simple and the multiple shooting methods. The Modified Simple Shooting Method (MSSM) sheds undesirable aspects of both previously mentioned methods to yield a superior, faster method for solving TPBVPs. The convergence of the Modified Simple Shooting Method is proven under mild conditions on the TPBVP. A comparison of the multiple and the modified simple shooting methods is made for some cases where both methods converge. Finally, we study a TPBVP arising from Pontryagin's Maximum principle applied to an six-degree-of-freedom aircraft model, for which the MSSM converges while the MSM fails to converge.Item An edge-of-the-wedge theorem without wedges(Texas Tech University, 1977-05) Olivier, Philip DenisNot availableItem An expansion theorem for a class of non-self-adjoint boundary value problems(Texas Tech University, 1968-08) Drummond, John CNot availableItem An initial-boundary value problem for parabolic systems(Texas Tech University, 1980-12) Fuente, Maria ConcepcionNot availableItem Application of boundary element method for some 3-D elasticity problems(Texas Tech University, 1985-08) Hong, KappyoNot availableItem Application of the boundary element method for soil structure interaction problems(Texas Tech University, 1985-12) Sivakumar, JayaramanSoil-structure interaction problems are those in which the behavior of the structure and the behavior of the soil surrounding it are interdependent, and the solution requires the analysis of both the structure and the soil in a compatible manner. Modeling of soil is very complicated and approximations are made purely on the experience and judgment of the engineer. So far, because of the simplicity of the concept, Winkler's Model is being used extensively in soilstructure interaction problems. Closed form solutions are available only for simple geometry and loading conditions, thereby restricting the analysts to idealize the problem. There are improved models developed by Pasternak, Vlasov and Leontiev, adding complexities in calculations. The drawback in these analyses is the nonunique value of the coefficient of subgrade reaction of the soil. Recently, the finite element method has been used to solve these problems. Here the advantage of modeling the problem is offset by the tedium in the preparation of input data for the analysis. It is in this context that the boundary element method is used in this research for application in some soil-structure interaction problems. In this work, the structure is represented by finite elements and the soil medium by boundary elements. The soil stiffness matrix is developed and condensed up to the interface. This matrix is efficiently transformed and coupled to the structure stiffness matrix for complete analysis. Computer programs have been developed in two and three dimensional elasticity for application to typical soilstructure interaction problems. Also, a condensation procedure has been suggested for analyzing layered soil media. The results compare favorably with complete finite element analysis. The elastic constants of the materials are sufficient for the analysis, thereby totally avoiding the value of the coefficient of subgrade reaction. Thus, the codes developed establish their superiority for implementation in soil-structure interaction problems. This procedure is a starting step in geotechnical problems for an accurate and rational analysis to replace the semiempirical relations presently in use.Item Application of the boundary element method for tornado forces on buildings(Texas Tech University, 1985-08) Selvam, Rathinam PanneerNot availableItem Computation of eigenlengths of singular two point boundary value problems by invariant imbedding(Texas Tech University, 1979-05) Elder, Ira ThurmanNOT AVAILABLEItem Dynamics of boundary-controlled convective reaction-diffusion equations(Texas Tech University, 1995-05) Okasha, Nahed AThis research is concerned with an initial value boundary problem for a class of convective reaction-diffusion equations for which a feedback control law is implemented through the boundary conditions. This class contains, as a special case the well-known Burgers' equation which has been studied rather extensively. Using methods based on Functional Analysis, in particular, the energy method and Galerkin Approximations, solvability for the above class is established. In addition, we prove the global in time existence and the regularity of solutions of the controlled problem for sufficiently small L^2-initial data. To do this, additional explicit restrictions on the nonlinear terms are imposed. Then we prove the local Lyapunov stability of the system, the existence of an absorbing ball, and the existence of a compact local attractor in this ball. Similar results for the same equation with Dirichlet boundary conditions are obtained for arbitrary L^2-initial data. The solutions of the boundary-controlled problem are shown to depend continuously on the boundary control parameters. As these parameters tend to infinity, we prove that the trajectories of the boundary-controlled problem converge, uniformly on any finite interval, to the trajectories of the corresponding problem with Dirichlet boundary conditions.Item Heat conduction in a three-dimensional body with moving boundaries(Texas Tech University, 1983-05) Shah, Jitendrakumar KanubhaiIn this study, three-dimensional heat conduction problems with moving and nonmoving grid and the problems of a body undergoing phase change are solved. Unsteady heat conduction problems are solved using the body-fitted coordinate technique in two and three dimensions. A method of generating a moving grid structure in time asymptotic problems is applied here. Results presented show significant error reduction for the two- and three - dimensional heat conduction equations when compared with the nonmoving grid solution. Phase - change problems are solved for the case or sublimation, but the technique can be extended to other phase-change problems. Techniques presented for the two dimensional cases are shown to extend directly to the three-dimensional cases without major difficulties. The biggest difference between the two- and three – dimensional work is the large increase in computational time necessary for the three-dimensional problems.Item Local elliptic boundary value problems for the dirac operator(2006) Scholl, Matthew Gregory; Freed, DanItem Local feedback regularization of three-dimensional Navier-Stokes equations on bounded domains(Texas Tech University, 1997-05) Balogh, AndrasThe specific problem we consider here is inspired by recent advances in the control of nonlinear distributed parameter systems and its possible applications to hydrodynamics. The main objective is to investigate the extent to which the 3-dimensional Navier-Stokes system can be regularized using a particular, physically motivated, feedback control law. The specific choice of feedback mechanism is motivated by a work of O.A. Ladyzhenskaya [7] in which she introduces a modification of the Navier-Stokes equation on a three dimensional bounded domain and shows that the resulting perturbed system possesses global dynamics and, furthermore, this dynamics is stable. It is in this sense that we understand the system to be regularized.Item Numerical Solution of Heat Conduction Problems with a Change of Phase(Texas Tech University, 1981-05) Roberts, David LNot Available.Item Numerical solution of heat conduction problems with a change of phase(Texas Tech University, 19819-12) Roberts, David LNumerical solutions for the freezing of finite slabs, cylinders, and spheres initially above the fusion temperature subject to boundary conditions of the first, second, and third kind were obtained by utilizing the DuFort-Frankel finite-difference scheme. Illustrative calculations for the transient temperature field, freezing front location, heat flux at the wall, and times for complete freezing were presented for various values of the dimensionless parameters. The ranges of values for the dimensionless parameters for which solutions can be successfully obtained were determined. FORTRAN IV computer programs which can be used to obtain solutions for any conditions within these ranges have been made available. The computer programs were written in such a way as to be easily extended and/or modified to solve other freezing problems.Item Numerical solutions of an observability problem for the heat equation(Texas Tech University, 1988-12) Anglin, Quanna LeahIn this thesis we will consider numerical solutions to the discrete observability problem of the heat equation with periodic boundary conditions. The problem to be discussed is that of one-dimensional circular geometry, modeled by an insulated ring of wire. It is known that the discrete observability of the heat equation is preserved by two appropriately chosen spatial samples and an infinite set of discrete temporal samples. The main result of this thesis is a numerical examination of this result.Item Item Regularity of free boundary in variational problems(2005) Teixeira, Eduardo Vasconcelos Oliveira; Caffarelli, Luis A.We study the existence and geometric properties of an optimal configurations to a variational problem with free boundary. More specifically, we analyze the nonlinear optimization problem in heat conduction which can be described as follows: given a surface ∂D ⊂ R n and a positive function ϕ defined on it (temperature distribution of the body D), we want to find an optimal configuration Ω ⊃ ∂D (insulation), that minimizes the loss of heat in a stationary situation, where the amount of insulating material is prescribed. This situation also models problems in electrostatic, potential flow in fluid mechanics among others. The quantity to be minimized, the flow of heat, is given by a monotone operator on the flux uµ. Mathematically speaking, let D ⊂ R n be a given smooth bounded domain and ϕ: ∂D → R+ a positive continuous function. For each domain Ω surrounding D such that Vol.(Ω \ D) = 1, we consider the potential associated to the configuration Ω, i.e., the harmonic function on Ω\D taking boundary data u ∂D ≡ ϕ and u ∂Ω ≡ 0, and compute J(Ω) := Z ∂D Γ(x,uµ(x))dσ, vii where µ is the inward normal vector defined on ∂D and Γ is a continuous family of convex functions. Our goal is to study the existence and geometric properties of an optimal configuration related to the functional J. In other words, our purpose is to study the problem: minimize { J(u) := Z ∂D Γ(x,uµ(x))dσ : u: DC → R, u = ϕ on ∂D, ∆u = 0 in {u > 0} and Vol.(supp u) = 1 } Among other regularity properties of an optimal configuration, we prove analyticity of the free boundary up to a small singular set. We also establish uniqueness and symmetry results when ∂D has a given symmetry. Full regularity of the free boundary is obtained under these symmetry conditions imposed on the fixed boundary.Item The first boundary value problem for x" = F(x, x', t)(Texas Tech University, 1971-05) Tippett, James MiltonNot availableItem The mathematics of interpolation and sampling(Texas Tech University, 1986-08) Smith, Jennifer KIn this thesis, continuous time, autonomous, observable dynamical systems are studied. The main problem considered is whether sampling at discrete times preserves observability. The discrete observability problem is shown to be equivalent to the general theory of linear interpolation. The mathematical theory used in this paper is Polya's property W which is used to produce several new results. In addition, the problem of discrete sampling is also interpreted as an n-point boundary value problem and as a problem of independence in the dual space.Item The Nonlinear Integrodifferential Initial-Value Problem for the Reflection Kernel of an Isotropically Scattering Slab: Direct Existence Proofs(Texas Tech University, 1985-05) Juang, JonqNot Available.