Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 126 for “"algebraic equations"”.
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Applications and numerical investigation of differential-algebraic equations
Differential-algebraic equations (DAEs) result in many areas of science and engineer- ing. In this thesis, numerical methods for solving DAEs are compared for two prob- lems, energy-economic models and traffic flow models. An energy-economic model is presented based on the Hubbert model of oil …
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Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations
The algebraic constraints in a system of differential-algebraic equations (DAEs) impose a consistency requirement on the initial values that can be difficult to satisfy. In this thesis the consistency requirement is characterized by a system of equations. An approximation method is introduced for …
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Systems of Nonlinear Algebraic Equations Arising in Simulation of Semiconductor Devices
… of the system of elliptic partial differential equations that model a semiconductor device. We use standard finite difference methods to discretize these equations and derive systems of nonlinear equations. Due to the extremely large number of unknowns it is prohibitively expensive to use …
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Theory and Application of a Class of Abstract Differential-Algebraic Equations
… existence of solutions for ordinary differential-algebraic equations (DAEs). Because of the geometric and operator-theoretic aspects of this particular method, it can be extended to the case of infinite-dimensional abstract DAEs. For example, partial differential equations (PDEs) are often …
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Approximations for Nonlinear Differential Algebraic Equations to Increase Real-time Simulation Efficiency
… the solution of a set of coupled differential algebraic equations (DAE). DAE's are not conducive to real-time implementation such as in a driving simulator, without a very expensive processing capability. The primary objective of this thesis is to show that multi-body models constructed from …
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Waveform relaxation methods for the simulation of systems of differential algebraic equations with applications to electric power systems
… are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical and chemical …
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An analysis of teachers‟ exemplary instructional strategies in relation to NSSCO learners‟ learning difficulties in solving algebraic equations in Omaruru circuit
… NSSCO learners‟ learning difficulties in solving Algebraic equations in Omaruru Circuit, Erongo Educational Region, Namibia. This study used Cognitive Constructivism Theory as its theoretical underpinnings. The study applied a convergent mixed method, QUAN and QUAL, approach, using a …
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A modeling framework and toolset for simulation and characterization of the cochlea within the auditory system
… These models are formulated as differential algebraic equations, and solved for impulse and tone excitations to determine responses. The solutions are mapped into tuning characteristics as a function of position within the cochlear partition. Objectives The central objective of simulation is …
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Conservation and efficiency in least squares finite element methods
… the numerical solution of partial differential equations include accurate discretizations and efficient solutions of the algebraic equations. With respect to discretizations, conservation is often sought after. However, least-squares finite element methods are known to be not mass conserving …
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An analytic solution for the stress distribution in a semi- infinite strip loaded on the transverse edge
… conditions are adjusted, a system of integral equations and a system of algebraic equations are obtained, which are further reduced. to a single system of algebraic equations. The latter system is solved by the method of successive approximations. In each case, the expressions for normal …
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Errors and misconceptions related to learning algebra in the senior phase – grade 9
… that explains the rules of symbol operations, equations, and inequality. Algebra is a combination of logic and language; hence common mistakes and conceptions are either attributed to logic or language problems, or both. There is also ongoing debate about the fact that learners come to class …
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Exploiting compression in solving discretized linear systems
Solving systems of linear algebraic equations is crucial for many computational problems in science and engineering. Numerous techniques are available for solving such linear systems, including direct methods such as Gaussian elimination and iterative methods such as GMRES. This thesis proposes a …
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Optimal Linear Feedback Control for Incompressible Fluid Flow
… is considered for large systems of differential algebraic equations arising from discretization of saddle point problems. Necessary conditions are derived by applying the Maximum Principle and have the form of constrained Riccati equations. We consider two approaches for solving the feedback …
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Periodic Solutions of Chaotic Partial Differential Equations With Symmetries
… solutions of chaotic partial differential equations with symmetries. Relative time-periodic solutions are solutions which are periodic in time, up to a transformation by an element of the equations' symmetry group. First, we work with the complex Ginzburg-Landau equation (CGLE) as a model …
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Modellbasierte Diagnose auf Basis Differential-Algebraischer Systeme mit Nichtlinearen Kalman-Filtern
… considers the models formulated as Differential-Algebraic Equations (DAE) for the model-based diagnosis. <br /><br /> The foundation for the development of the diagnosis methods is the state estimation with nonlinear Kalman-filters. Consequently, the state estimation approaches as well as the …
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Dynamic Security Assessment of Power Systems Using Trajectory Sensitivity Approach
… handle complex models such as differential algebraic equations (DAE), discrete event coupled with DAE, and even hybrid systems. On the other hand, this approach suffers from the requirement of additional computation of the sensitivities. Nevertheless, this approach has provided useful …
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An augmented Jacobian matrix algorithm for tracking homotopy zero curves
… zeros or fixed points of nonlinear systems of (algebraic) equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set …
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Generalized BDF methods applied to Hessenberg form DAEs
… solution of Hessenberg form differential algebraic equations by variable stepsize generalized backward difference formulae (GBDF). GBDF methods of sufficiently high order are shown to converge for problems of index two, three, or four. The proof techniques developed are not sufficiently …
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Analysis of an oscillating engine for power generation based on the "Drinking Bird Toy"
… The mathematical model resulted in seven linear algebraic equations to be solved simultaneously. The iterative nature of the calculations necessitated the use of the University of Missouri at Columbia IBM36O digital computer. The calculations were performed for Freon-11 as internal working fluid. …
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