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Showing 1 to 20 of 23 for “"COLLOCATION METHODS"”.
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Improved collocation methods with application to direct trajectory optimization
Improved collocation methods for the solution of a set of ordinary differential equations are developed and used to solve minimum-time, Earth-moon orbit transfers. These collocation methods are based on a family of modified Gaussian quadrature rules. This family of rules includes the basic …
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Numerical Solution of Stiff Ordinary Differential Equations Using Collocation Methods
Made available in DSpace on 2014-12-13T18:01:52Z (GMT). No. of bitstreams: 1 7709075.pdf: 2874498 bytes, checksum: 35500be9b4b4d0fe80f9e6e16eb670ad (MD5) Previous issue date: 1976
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Improved Collocation Methods With Application to Six -Degree -of -Freedom Trajectory Optimization
An improved collocation method is developed for a class of problems that is intractable, or nearly so, by conventional collocation. These are problems in which there are two distinct timescales of the system states, that is, where a subset of the states have high-frequency variations while the …
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ΜΕΘΟΔΟΙ ΠΑΡΕΜΒΟΛΗΣ ΜΕ Ο(Η6) ΣΥΓΚΛΙΣΗ ΓΙΑ ΕΛΛΕΙΠΤΙΚΕΣ ΕΞΙΣΩΣΕΙΣ 2ΗΣ ΚΑΙ 4ΗΣ ΤΑΞΗΣ
IN THIS THESIS WE DEVELOP AND ANALYZE OPTIMAL COLLOCATION METHODS FOR SECOND AND FOURTH ORDER TWO-POINT BOUNDARY VALUE PROBLEMS (LINEAR AND NON LINEAR). THESEDIFFERENTIAL EQUATIONS ARE CONSIDERED TO BE DEFINED IN SPACES R AND R2 AND THEIR SOLUTION SATISFIES SOME BOUNDARY CONDITIONS. THE …
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Hydrodynamic Stability of the boundary layer beneath a Stokes wave
… the boundary layer. Using Fourier and Chebyshev collocation methods to solve the Orr-Sommerfeld eigenvalue problem, we examine the stability of the flow across a broader parameter space. Our findings suggest that, while the laminar boundary layer remains stable for the momentary stability …
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Chebyshev spectral methods for potential field computation
We investigate Chebyshev spectral methods for solving Poisson's equation and the generalized Poisson's equations and apply them to 3-D gravity and DC resistivity modeling. When we approximate a function by a finite sum of Chebyshev polynomials, there are two kinds of errors: truncation and …
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Analytical and numerical techniques for wave scattering
… classed into two categories: analytically based methods which use special transforms and functions to provide a near-complete mathematical description of the scattering process, and numerical techniques which select an approximate solution from a general finite-dimensional space of possible …
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A reduced-basis method for input-output uncertainty propagation in stochastic PDEs
… through random media. Monte-Carlo based sampling methods, generalized polynomial chaos and stochastic collocation methods are some of the popular approaches that have been used in the analysis of such problems. This work proposes a non-intrusive reduced-basis method for the rapid and reliable …
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Wavelets operational methods for fractional differential equations and systems of fractional differential equations
In this thesis, new and effective operational methods based on polynomials and wavelets for the solutions of FDEs and systems of FDEs are developed. In particular we study one of the important polynomial that belongs to the Appell family of polynomials, namely, Genocchi polynomial. This polynomial …
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Numerical solution of fractional partial differential equations by spectral methods
… modeling of physical models by using spectral methods. In the last few decades, spectral methods have been developed for the solution of time and space dimensional FPDEs. There are different types of spectral methods such as collocation methods, Tau methods and Galerkin methods. This research …
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Modeling and Simulation of Molecular Couette Flows and Related Flows
… solved with high precision by using Chebyshev collocation and chunk-based collocation methods. The velocity profiles of gaseous Couette flows and related flows with a wide range of Knudsen number and the Maxwell boundary condition of various accommodation ratios are obtained. Moreover, the …
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Trajectory optimization and data-driven modeling for robotic bat flapping flight
… approach that uses this model with direct collocation methods to plan dynamically feasible flight maneuvers. We demonstrate a range of different maneuvers including a launch to an altitude, a banked turn, and a launch, dive, and recover maneuver. The launch to an altitude and launch, dive, …
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A Technique for Solving the Singular Integral Equations of Potential Theory
… simple. Previous works based on classical methods have yielded solutions only for very special cases while contemporary methods such as finite differences, finite elements and boundary element techniques are computationally extensive. Since the two-dimensional integral equations of interest …
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DENSITY BASED FRAMEWORKS FOR SPATIO-TEMPORAL CHANGE ANALYSIS
… research is the development of density-based collocation mining frameworks. As density functions have been demonstrated to be an efficient tool to model the distance-decay effect, we developed new density-based collocation measures estimating the strength of a given collocation pattern in a …
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Learning Nonlinear Dynamics: Methods and Applications
… developing robust, scalable, and interpretable methods for learning nonlinear ordinary differential equations (ODEs) and partial differential equations (PDEs) directly from data, with a particular emphasis on applications in fluid dynamics. In Chapter 2, we introduce a novel methodology for …
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A Variational Approach to Estimating Uncertain Parameters in Elliptic Systems
… these numerically. Lastly, we illustrate our methods by means of numerical examples.
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Stability Analysis of Time Delay Systems Using Spectral Element Method
… limited to autonomous DDEs. Moreover, the methods that are suitable for non-autonomous DDEs, e.g. the Semi-discretization approach, often result in a very large system of algebraic equations that can cause computational difficulties. Collocation-type methods, such as Chebyshev-collocation …
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Spectral Methods For The Hamiltonian Systems
<p>We conduct a systematic comparison of spectral methods with some</p> <p>symplectic methods in solving Hamiltonian dynamical systems. Our</p> <p>main emphasis is on the non-linear problems. Numerical evidence has</p> <p>demonstrated that the proposed spectral collocation method preserves</p> …
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On the application of numerical continuation to large-scale dynamical systems
… in this code compatible with the asynchronous collocation toolbox in coco. The asynchronous collocation toolbox developed in this dissertation extends the capability of common implementation of collocation methods for differential equations by reducing the number of mesh points required …
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