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Second order dynamic equations on time scalesWeiss, Jacob. January 1900 (has links)
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2007. / Title from title screen (site viewed May 20, 2008). PDF text: 77 p. ; 328 K. UMI publication number: AAT 3284240. Includes bibliographical references. Also available in microfilm and microfiche formats.
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Modelling, control and locomotion of a twelve degree of freedom biped robotAkdas, Davut January 2001 (has links)
No description available.
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Non-standard finite difference methods in dynamical systemsKama, Phumezile. January 2009 (has links)
Thesis (Ph.D..(Mathematics and Applied Mathematics)) -- University of Pretoria, 2009. / Summary and abstract in English. Includes bibliographical references.
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Solving higher order dynamic equations on time scales as first order systemsDuke, Elizabeth R. January 2006 (has links)
Theses (M.A.)--Marshall University, 2006. / Title from document title page. Includes abstract. Document formatted into pages: contains vii, 72 pages. Bibliography: p. 70-72.
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Preconditioning techniques for all-at-once linear systems arising from advection diffusion equationsLin, Xuelei 07 August 2020 (has links)
In this thesis, we mainly study preconditioning techniques for all-at-once linear systems arising from discretization of three types of time-dependent advection-diffusion equation: linear diffusion equation, constant-coefficients advection-diffusion equation, time-fractional sub-diffusion equation. The proposed preconditioners are used with Krylov subspace solvers. The preconditioner developed for linear diffusion equation is based on -circulant ap- proximation of temporal discretization. Diagonalizability, clustering of spectrum and identity-plus-low-rank decomposition are derived for the preconditioned matrix. We also show that generalized minimal residual (GMRES) solver for the preconditioned system has a linear convergence rate independent of matrix-size. The preconditioner for constant-coefficients advection-diffusion equation is based on approximating the discretization of advection term with a matrix diagonalizable by sine transform. Eigenvalues of the preconditioned matrix are proven to be lower and upper bounded by positive constants independent of discretization parameters. Moreover, as the preconditioner is based on spatial approximation, it is also applicable to steady-state problem. We show that GMRES for the preconditioned steady-state problem has a linear convergence rate independent of matrix size. The preconditioner for time-fractional sub-diffusion equation is based on approximat- ing the discretization of diffusion term with a matrix diagonalizable by sine transform. We show that the condition number of the preconditioned matrix is bounded by a constant independent of discretization parameters so that the normalized conjugate gradient (NCG) solver for the preconditioned system has a linear convergence rate independent of discretization parameters and matrix size. Fast implementations based on fast Fourier transform (FFT), fast sine transform (FST) or multigrid approximation are proposed for the developed preconditioners. Numerical results are reported to show the performance of the developed preconditioners
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Preconditioning techniques for all-at-once linear systems arising from advection diffusion equationsLin, Xuelei 07 August 2020 (has links)
In this thesis, we mainly study preconditioning techniques for all-at-once linear systems arising from discretization of three types of time-dependent advection-diffusion equation: linear diffusion equation, constant-coefficients advection-diffusion equation, time-fractional sub-diffusion equation. The proposed preconditioners are used with Krylov subspace solvers. The preconditioner developed for linear diffusion equation is based on -circulant ap- proximation of temporal discretization. Diagonalizability, clustering of spectrum and identity-plus-low-rank decomposition are derived for the preconditioned matrix. We also show that generalized minimal residual (GMRES) solver for the preconditioned system has a linear convergence rate independent of matrix-size. The preconditioner for constant-coefficients advection-diffusion equation is based on approximating the discretization of advection term with a matrix diagonalizable by sine transform. Eigenvalues of the preconditioned matrix are proven to be lower and upper bounded by positive constants independent of discretization parameters. Moreover, as the preconditioner is based on spatial approximation, it is also applicable to steady-state problem. We show that GMRES for the preconditioned steady-state problem has a linear convergence rate independent of matrix size. The preconditioner for time-fractional sub-diffusion equation is based on approximat- ing the discretization of diffusion term with a matrix diagonalizable by sine transform. We show that the condition number of the preconditioned matrix is bounded by a constant independent of discretization parameters so that the normalized conjugate gradient (NCG) solver for the preconditioned system has a linear convergence rate independent of discretization parameters and matrix size. Fast implementations based on fast Fourier transform (FFT), fast sine transform (FST) or multigrid approximation are proposed for the developed preconditioners. Numerical results are reported to show the performance of the developed preconditioners
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Tight Approximability Results for the Maximum Solution Equation Problem over Abelian GroupsKuivinen, Fredrik January 2005 (has links)
<p>In the maximum solution equation problem a collection of equations are given over some algebraic structure. The objective is to find an assignment to the variables in the equations such that all equations are satisfied and the sum of the variables is maximised. We give tight approximability results for the maximum solution equation problem when the equations are given over finite abelian groups. We also prove that the weighted and unweighted versions of this problem have asymptotically equal approximability thresholds.</p><p>Furthermore, we show that the problem is equally hard to solve as the general problem even if each equation is restricted to contain at most three variables and solvable in polynomial time if the equations are restricted to contain at most two variables each. All of our results also hold for the generalised version of maximum solution equation where the elements of the group are mapped arbitrarily to non-negative integers in the objective function.</p>
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Experimental investigation of a time scales linear feedback control theoremAllen, Benjamin T. Gravagne, Ian A. January 2007 (has links)
Thesis (M.S.E.C.E.)--Baylor University, 2007. / Includes bibliographical references (p. 99).
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Hamilton's equations with Euler parameters for hybrid particle-finite element simulation of hypervelocity impactShivarama, Ravishankar Ajjanagadde. January 2002 (has links) (PDF)
Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.
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Investigation of a coupled Duffing oscillator system in a varying potential field /O'Day, Joseph Patrick. January 2005 (has links)
Thesis (M.S.)--Rochester Institute of Technology, 2005. / Typescript. Includes bibliographical references (leaves 144-146).
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