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921.
1 Introduction Wornell and Oppenheim[1,2] first proposed a modulation technique as an interesting potential application of dy-homogeneous signals. Due to the fractal properties of the homogeneous signals, this technique is called fractal modulation afterwards. This class of homogeneous signals remains invariant under scaling of the time axis. Dy-homogeneous signals satisfy the dyadic self-similarity property[3] s (t ) = 2 kH s (2 kt) (1) For all integers k and a constant H, termed the degree… 相似文献
922.
In this work we propose and analyze a fully discrete modified Crank–Nicolson finite element (CNFE) method with quadrature for solving semilinear second‐order hyperbolic initial‐boundary value problems. We prove optimal‐order convergence in both time and space for the quadrature‐modified CNFE scheme that does not require nonlinear algebraic solvers. Finally, we demonstrate numerically the order of convergence of our scheme for some test problems. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
923.
G. López Lagomasino L. Reichel L. Wunderlich 《Linear algebra and its applications》2008,429(10):2540-2554
Many problems in science and engineering require the evaluation of functionals of the form Fu(A)=uTf(A)u, where A is a large symmetric matrix, u a vector, and f a nonlinear function. A popular and fairly inexpensive approach to determining upper and lower bounds for such functionals is based on first carrying out a few steps of the Lanczos procedure applied to A with initial vector u, and then evaluating pairs of Gauss and Gauss-Radau quadrature rules associated with the tridiagonal matrix determined by the Lanczos procedure. The present paper extends this approach to allow the use of rational Gauss quadrature rules. 相似文献
924.
A new family of locally conservative cell‐centred flux‐continuous schemes is presented for solving the porous media general‐tensor pressure equation. A general geometry‐permeability tensor approximation is introduced that is piecewise constant over the subcells of the control volumes and ensures that the local discrete general tensor is elliptic. A family of control‐volume distributed subcell flux‐continuous schemes are defined in terms of the quadrature parametrization q (Multigrid Methods. Birkhauser: Basel, 1993; Proceedings of the 4th European Conference on the Mathematics of Oil Recovery, Norway, June 1994; Comput. Geosci. 1998; 2 :259–290), where the local position of flux continuity defines the quadrature point and each particular scheme. The subcell tensor approximation ensures that a symmetric positive‐definite (SPD) discretization matrix is obtained for the base member (q=1) of the formulation. The physical‐space schemes are shown to be non‐symmetric for general quadrilateral cells. Conditions for discrete ellipticity of the non‐symmetric schemes are derived with respect to the local symmetric part of the tensor. The relationship with the mixed finite element method is given for both the physical‐space and subcell‐space q‐families of schemes. M‐matrix monotonicity conditions for these schemes are summarized. A numerical convergence study of the schemes shows that while the physical‐space schemes are the most accurate, the subcell tensor approximation reduces solution errors when compared with earlier cell‐wise constant tensor schemes and that subcell tensor approximation using the control‐volume face geometry yields the best SPD scheme results. A particular quadrature point is found to improve numerical convergence of the subcell schemes for the cases tested. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
925.
一类非线性偏积分微分方程二阶差分全离散格式 总被引:1,自引:0,他引:1
给出了数值求解一类非线性偏积分微分方程的二阶全离散差分格式.采用了二阶向后差分格式,积分项的离散利用了Lubich的二阶卷积求积公式,给出了稳定性的证明、误差估计及收敛性的结果. 相似文献
926.
We consider the problem of approximately reconstructing a function f defined on the surface of the unit sphere in the Euclidean space ℝq +1 by using samples of f at scattered sites. A central role is played by the construction of a new operator for polynomial approximation, which is a uniformly bounded quasi‐projection in the de la Vallée Poussin style, i.e. it reproduces spherical polynomials up to a certain degree and has uniformly bounded Lp operator norm for 1 ≤ p ≤ ∞. Using certain positive quadrature rules for scattered sites due to Mhaskar, Narcowich and Ward, we discretize this operator obtaining a polynomial approximation of the target function which can be computed from scattered data and provides the same approximation degree of the best polynomial approximation. To establish the error estimates we use Marcinkiewicz–Zygmund inequalities, which we derive from our continuous approximating operator. We give concrete bounds for all constants in the Marcinkiewicz–Zygmund inequalities as well as in the error estimates. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
927.
James V. Lambers 《Numerical Algorithms》2009,51(2):239-280
This paper presents modifications of Krylov Subspace Spectral (KSS) Methods, which build on the work of Gene Golub and others pertaining to moments and Gaussian quadrature to produce high-order accurate approximate solutions to the time-dependent Schrödinger equation in the case where either the potential energy or the initial data is not a smooth function. These modifications consist of using various symmetric perturbations to compute off-diagonal elements of functions of matrices. It is demonstrated through analytical and numerical results that KSS methods, with these modifications, achieve the same high-order accuracy and possess the same stability properties as they do when applied to parabolic problems, even though the solutions to the Schrödinger equation do not possess the same smoothness. 相似文献
928.
Mathematical Modelling on the Quadrature Error of Low-rate Microgyroscope for Aerospace Applications
Bao Y. Yeh Yung C. Liang Francis E. H. Tay 《Analog Integrated Circuits and Signal Processing》2001,29(1-2):85-94
This paper presents the mathematical modelling on the quadrature error of a microgyroscope due to the imbalance of the asymmetric spring flexures. Quadrature error occurs when the proof mass of a microgyroscope oscillates along an axis that is not exactly parallel to the lateral-axis. The imbalance due to manufacturing variation can cause the proof mass to rotate when a force acts on the proof mass. The proposed mathematical model was verified by the finite element software IntelliCAD, and found to have a good agreement on angles of rotation of comb fingers. The mathematical model provides a new avenue in evaluating the quadrature error system and in saving the overall simulation time. 相似文献
929.
B. Bialecki M. Ganesh K. Mustapha 《Numerical Methods for Partial Differential Equations》2005,21(5):918-937
We propose and analyze an application of a fully discrete C2 spline quadrature Petrov‐Galerkin method for spatial discretization of semi‐linear parabolic initial‐boundary value problems on rectangular domains. We prove second order in time and optimal order H1 norm convergence in space for the extrapolated Crank‐Nicolson quadrature Petrov‐Galerkin scheme. We demonstrate numerically both L2 and H1 norm optimal order convergence of the scheme even if the nonlinear source term is not smooth. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005. 相似文献
930.