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 30 for “"Legendre Polynomials"”.
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Glazman-Krein-Naimark theory, left-definite theory, and the square of the Legendre polynomials differential operator.
… theory associated with the classical Legendre self-adjoint second-order differential operator A in L² (−1, 1) which has the Legendre polynomials {Pn} ∞ n=0 as eigenfunctions. As a consequence, they explicitly determined the domain D(A2) of the self-adjoint operator A2 . However, this …
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Numerical solution of fractional partial differential equations by spectral methods
… operational matrix methods via Genocchi polynomials and Legendre polynomials for the solution of two and three dimensional FPDEs. Moreover, in this study, Genocchi wavelet-like basis method and Genocchi polynomials based Ritz- Galerkin method have been derived to deal with FPDEs and …
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Development and Applications of Finite Elements in Time Domain
… Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, Hermite, Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of TFM, and the one often …
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The temperature distribution on a spherical shell in the presence of a primary radiative source and a reflecting and radiating infinite plane
… to the linearized equation is found in terms of Legendre polynomials and associated Legendre functions. Then some numerical results are obtained for which selected problem parameters are varied.
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Error analysis of higher order time-domain finite element methods for the one-dimensional Maxwell's equations
… accuracy. Fifth-order spatial integration using Legendre polynomials, so spatial errors will be much smaller than temporal errors.
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Domain partitioning to bound moments of differential equations using semidefinite optimization
… equations including the Bessel ODE, and Legendre polynomials. In the two-dimensional case we have demonstrated the algorithm by calculating bounds on various PDEs including the Helmholtz equation, and heat equation. In both cases, the results were encouraging with tighter bounds on …
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Methods for recognizing patterns in digitized line drawings
… of a spline approximation of the line data and Legendre polynomials. Some methods for recognizing incomplete line patterns and partially occluded curves are also discussed, and some experiments are performed.
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Image feature matching using polynomial representation of chain codes
… is based on a truncated series of orthogonal polynomials used to represent a piecewise continuous function derived from a chain code. This piecewise continuous function is generated from a chain code by mapping individual chain links onto real numbers. A variety of alternative mappings of …
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Thickness and strain determinations of thin film systems by x-ray analysis
… of the angular range in chi could be fitted with Legendre polynomials and extrapolated to chi=90°. The fitted orientation functions were then used to accurately calculate the thickness of the thin films. The method proved to be theoretically consistent. The residual strain measurements completed …
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Numerical Simulations Of Black Hole Binaries: Second Order Spectral Methods
… The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries as is typical in first-order formulations. Semi-discrete stability of the new method is proved using energy arguments for the scalar wave equation …
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An absolute measurement of the photodisintegration of deuterium
… The differential cross sections have been fit by Legendre polynomials. These results are in reasonable agreement with previous experiments and theoretical calculations.
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Dynamic measurement and characterization of Poisson's ratio
… the possible regressor set formed by products of Legendre polynomials in x and y, the two-dimensional coordinates of the beam. The resulting model is manipulated to extract the transverse and anticlastic radii of curvature of the beam which are then used to find local and global estimates of …
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On the origins of the ice ages : insolation forcing, age models, and nonlinear climate change
… full insolation forcing is also developed using Legendre polynomials to represent the spatial modes of variability and singular vectors to represent seasonal and long-term changes. The leading four spatial and temporal modes describe over 99% of the insolation variability making this a relatively …
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An absolute measurement of the photodisintegration of Helium-4
… distribution was fitted to an expansion of Legendre polynomials in cos <i>θ</i> including terms of order 0-3. This measurement is in agreement with a previous measurement, and improves on the precision of the total cross section from the previous measurement by a factor of 6. A comparison is …
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Periodic Solutions of Chaotic Partial Differential Equations With Symmetries
… a spectral-Galerkin method and trigonometric and Legendre polynomials to generate basis functions. Details about the procedure are discussed. For this problem, the system of nonlinear algebraic equations whose solutions yield the relative time-periodic orbits is very large and its Jacobian matrix …
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Caracterização dos motivos de descarte e estimativas de parâmetros genéticos para longevidade de vacas da raça holandês
… random regression models (RRM) with fifth-order Legendre polynomials. Heritability estimates ranged from low to high, depending on age and culling reason: age-related (0.17–0.38), functionality (0.04–0.52), economic (0.002–0.20), conformation (0.02–0.28), production (0.02–0.26), health …
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Discrete generalized multigroup theory and applications
… transport equation. Discrete orthogonal polynomials are used, in conjunction with the traditional multigroup representation, to expand the energy dependence of the angular flux into a set of flux moments. The leading (zeroth) order equation is identical to a standard coarse group …
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Modal Analysis of Axisymmetric Structures using Zernike Polynomials and Machine Learning
… plates. The Ritz method, utilizing Zernike and Legendre polynomials as trial functions, is implemented to enable free-vibration analysis without the meshing constraints typically associated with traditional finite element methods. This approach allows arbitrary stiffener placement while …
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A Posteriori Error Analysis of the Discontinuous Galerkin Method for Linear Hyperbolic Systems of Conservation Laws
… term of the local DG error, which is spanned by Legendre polynomials of degree p and p+1 when p-th degree polynomial spaces are used for the solution. For special hyperbolic systems, where the coefficient matrices are nonsingular, we show that the leading term of the error is spanned by (p+1)-th …
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