Results 291 to 300 of about 274,119 (324)
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Principles of Mimetic Discretizations of Differential Operators
2007Compatible discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. We provide a common framework for mimetic discretizations using algebraic topology to guide our analysis. The framework and all attendant discrete structures are put together by using two basic
Pavel B. Bochev, James M. Hyman
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2D Discrete Differential Operators for Periodic Functions
2019 15th Selected Issues of Electrical Engineering and Electronics (WZEE), 2019This paper presents novel types of discrete differential operators for two-variable functions, periodic for each variable. They determine values of derivatives, both the first- as well the second, by the values of the function itself in a set of points uniformly distributed over the periods.
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Stencils with isotropic discretization error for differential operators
Numerical Methods for Partial Differential Equations, 2006Summary: We derive stencils, i.e. difference schemes, for differential operators for which the discretization error becomes isotropic in the lowest order. We treat the Laplacian, bi-Laplacian (= biharmonic operator), and the gradient of the Laplacian both in two and three dimensions.
Patra, M., Karttunen, M.E.J.
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Discrete differential operators on irregular nodes (DDIN)
International Journal for Numerical Methods in Engineering, 2011AbstractA previous research made an integral mathematical contribution for obtaining local function interpolation using neighboring nodal values of the solution function. Subsequent researchers developed mesh‐free methods for Finite Element Method (FEM). This principle can also be used to obtain discrete differential operators on irregular nodes.
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Closed-Form Discretization of Fractional-Order Differential and Integral Operators
SSRN Electronic Journal, 2018This paper introduces a closed-form discretization of fractional-order differential or integral Laplace operators. The proposed method depends on extracting the necessary phase requirements from the phase diagram. The magnitude frequency response follows directly due to the symmetry of the poles and zeros of the finite z-transfer function.
Reyad El-Khazali, Tenreiro Machado
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Fredholmness vs. Spectral Discreteness for first-order differential operators
Proceedings of the American Mathematical Society, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some Partial Differential Operators with Discrete Spectra
1981We study selfadjoint realizations of the formal differential operator Tu = m −1 [(p 1 ,u x ) x + (p 2 u y ) y ] in the weighted Hilbert space L m 2 (Ω) where Ω is the square domain (0,1) × (0,1). Assuming m, p 1 , p 2 are positive and reasonably smooth and that singularities of T occur only along the boundaries x=0 or y=0, a variety of strictly ...
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The discrete eigenvalues for a class of integro-differential operators (II)
Transport Theory and Statistical Physics, 1991Summary: The integro-differential operator investigated in this paper is in a class of unbounded non-selfadjoint operators arising from various applied areas. Under more general assumptions, the existence of discrete eigenvalues of this kind of operators is shown by using linear operator theory in \(L_2\) spaces.
Wang, Wenlong, Yang, Mingzhu
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Singular differential operators with spectra discrete and bounded below
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1979SynopsisA weighted, formally self-adjoint ordinary differential operator l of order 2n is considered, and conditions are given on the coefficients of l which ensure that all self-adjoint operators associated with l have a spectrum which is discrete and bounded below. Both finite and infinite singularities are considered. The results are obtained by the
Hinton, Don B., Lewis, Roger T.
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A Discrete Differential Operator for Direction-based Surface Morphometry
2007 IEEE 11th International Conference on Computer Vision, 2007This paper presents a novel directional morphometry method for surfaces using first order derivatives. Non-directional surface morphometry has been previously used to detect regions of cortical atrophy using brain MRI data. However, evaluating directional changes on surfaces requires computing gradients to obtain a full metric tensor.
Maxime Boucher +3 more
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