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 44 for “"Ordinary Differential Equations (ODEs)"”.
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Introducing the Picard Method for Approximating Solutions of Differential Equations with Neural Networks
For decades, differential equations have been used to model various problems in the natural sciences and engineering. However, ordinary differential equations (ODEs) are usually not analytically solvable, so many numerical approaches have been developed to produce approximate solutions. More …
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A review of current Rough Volatility Methods
… implement the Rough Heston, fractional Riccati ordinary differential equations (ODEs) must be solved; and this requires numerical methods. Three such methods in order of increasing complexity are considered. Using the fractional Adam's numerical method, the Rough Heston model can be effected to …
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Unified Mathematical Modeling, Analysis and Simulation of COVID-19 and Ecological Processes
… using compartmental modeling frameworks based on ordinary differential equations (ODEs). First, we propose a mechanistic model to investigate the transmission dynamics of COVID-19, particularly focusing on the emergence and population-level impact of a post-acute sequela referred to as long COVID …
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Rapid Approximation of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis of Gaussian Node Placement
… stiffness has been introduced into systems of ordinary differential equations (ODEs) that arise from spatial discreti zation of partial differential equations (PDEs). The components of the solutions to these systems are coupled and changing at widely varying rates, which present problems for …
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Exponential integrators: tensor structured problems and applications
The solution of stiff systems of Ordinary Differential Equations (ODEs), that typically arise after spatial discretization of many important evolutionary Partial Differential Equations (PDEs), constitutes a topic of wide interest in numerical analysis. A prominent way to numerically integrate such …
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Probabilistic Approximation and Analysis Techniques for Bio-Pathway Models
… representing bio-pathways is through a system of ordinary differential equations (ODEs). However, calibrating and analyzing large ODE-based pathway models often requires a large number of numerical simulations. To address this issue, this thesis presents an approximation approach. This consists of …
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Chaos in models of double convection
… the derivation and analysis of low-order sets of ordinary differential equations (ODEs) that accurately describe the behaviour of a fluid in convective motion. A second-order set of ODEs is presented and analysed, and then related to a particular double convection problem (compressible convection …
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Towards security without secrets
… Model Physical Unclonable Functions based on ordinary differential equations (ODEs), a conjecture on the form of ODE integrators, and a formal reduction of PPUF security to this conjecture. This result is extended to compare analog and digital computing more generally. Finally, this thesis …
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Damage Development in Static and Dynamic Deformations of Fiber-Reinforced Composite Plates
… and matrix cracking. The three damage modes are modeled using the theory of internal variables and the delamination by postulating a failure envelope in terms of the transverse stresses; the damage degrades elastic moduli. The delamination of adjoining layers is simulated by the nodal …
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Asynchronous waveform relaxation methods for ordinary differential equations on multiprocessors
… significant speedup in solving large systems of Ordinary Differential Equations (ODEs.) Often, large systems of ODEs have components that vary with different rates. If numerical solution is computed for the system as a whole, the step size will limited by the fastest component. Multirate methods …
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Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays
Delay differential equations (DDEs) are often used to model systems with time-delayed effects, and they have found applications in fields such as climate dynamics, biosciences, engineering, and control theory. In contrast to ordinary differential equations (ODEs), the phase space associated even …
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Computational Tools for Molecular Networks in Biological Systems
… mathematics. Some theoreticians use systems of ordinary differential equations (ODEs) as the basis for mathematical modelling of molecular networks. This thesis develops algorithms for estimating molecular reaction rate constants within those mathematical models by fitting the models to …
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Coupled oscillators near resonance
… oscillators can be transformed to the same ordinary differential equations (ODEs). We consider two types of resonances: accidental and intrinsic. For an accidental resonance, we find that the dynamics near a resonance is a generalization of the standard Hamiltonian dynamics of two coupled …
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Constructing Mathematical Models of Gene Regulatory Networks for the Yeast Cell Cycle and Other Periodic Processes
… then translated into a mathematical model, using Ordinary Differential Equations (ODEs), to describe these entities and their interactions. The models currently describe gene regulatory interactions, but we are expanding to capture other events, such as phosphorylation and ubiquitination. To model …
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Mathematical modeling of infectious diseases
… models of infectious diseases that consist of ordinary differential equations (ODEs) and partial differential equations (PDEs). An ODE model is formulated to describe the dynamics of wild mosquitoes when Wolbachia-infected female and male mosquitoes are introduced in the wild as a biological …
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Mathematical modeling of molecular mechanisms governing cell cycle progression in Caulobacter crescentus and differentiation of immune system progenitor cells
… this molecular mechanism into a set of ordinary differential equations (ODEs), we acquired new insights into the behavior of differentiating GMP cells. Next, we explore the cell cycle of the model prokaryotic organism, Caulobacter crescentus. Caulobacter is a uniquely successful …
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Algorithms for Reconstructing and Reasoning about Chemical Reaction Networks
… which are typically simulated by converting to ordinary differential equations (ODEs), so that the goal is to closely reproduce the observed quantitative and qualitative behaviors of the modeled process. This thesis proposes two algorithmic problems related to the construction and comprehension …
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Multimethods for the Efficient Solution of Multiscale Differential Equations
Mathematical models involving ordinary differential equations (ODEs) play a critical role in scientific and engineering applications. Advances in computing hardware and numerical methods have allowed these models to become larger and more sophisticated. Increasingly, problems can be described as …
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MATLODE: A MATLAB ODE Solver and Sensitivity Analysis Toolbox
… for sensitivity analysis of models described by ordinary differential equations (ODEs). MATLODE implements two distinct approaches for sensitivity analysis: direct (via the tangent linear model) and adjoint. Within each approach, four families of numerical methods are implemented, namely explicit …
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Numerical methods for optimization problems in water flow and reactive solute transport processes of xenobiotics in soils
… unsaturated zone leads to instationary partial differential equations (PDEs) coupled with nonlinear ordinary differential equations (ODEs). 2. ECOFIT: An efficient method for parameter estimation of xenobiotics in soils: The parameter estimation problem constrained by PDEs and ODEs is …
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