Quadrature methods for highly oscillatory linear and nonlinear systems of ordinary differential equations: part I

This work presents methods of efficient numerical approximation for linear and nonlinear systems of highly oscillatory ordinary differential equations. We show how an appropriate choice of quadrature rule improves the accuracy of approximation as the frequency of oscillation grows. We present asymptotic and Filon-type methods to solve highly oscillatory linear systems of ODEs, and WRF method, representing a special combination of Filon-type methods and waveform relaxation methods, for nonlinear systems. Numerical examples support this paper. Dedicated to the memory of Rudolf Khanamiryan. AMS subject classification (2000)  65L05, 34E05, 34C15     

The best quadrature formula based on Hermite information for the class KW~2[a,b]

The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.     

A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon

A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three‐points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved for a scheme based on the product two‐point Gaussian quadrature by establishing a relation with an underdetermined orthogonal spline collocation scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

加细函数正交性的一个判别准则

In this note, a criterion for orthonormality of refinable functions via characteristicpolynomial of a matrix is given.     

Numerical treatment of retarded boundary integral equations by sparse panel clustering

Stefan Sauter Institute for Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ^{We consider the wave equation in a boundary integral formulation.The discretization in time is done by using convolution quadraturetechniques and a Galerkin boundary element method for the spatialdiscretization. In a previous paper, we have introduced a sparseapproximation of the system matrix by cut-off, in order to reducethe storage costs. In this paper, we extend this approach byintroducing a panel clustering method to further reduce thesecosts.}     

A Generalization of Ostrowski Integral Inequality for Mappings Whose Derivatives Belong to L_1 [a,b] and Applications in Numerical Integration

A generalization of Ostrowski integral inequality for mappings whose derivatives belong to L_1 [a,b], and applications for general quadrature formulae are given.     

A 2.4GHz Quadrature Output Frequency Synthesizer

A design and implementation for a 2.4GHz quadrature output frequency synthesizer intended for bluetooth in 0.35μm CMOS technology are presented.A differentially controlled quadrature voltage-controlled oscillator (QVCO) is employed to generate quadrature (I/Q) signals.A second-order loop filter,with a unit gain transconductance amplifier having the performance of a third-order loop filter,is exploited for low cost.The measured spot phase noise is –106.15dBc/Hz@1MHz.Close-in phase noise is less than -70dBc/Hz.The synthesizer consumes 13.5mA under a 3.3V voltage supply.The core size is 1.3mm×0.8mm.     

旋转压电纳米梁的振动分析

本文基于非局部弹性理论，对旋转压电纳米梁模型的振动进行了分析．首先由哈密顿原理导出旋转压电纳米梁的动力学控制方程及相应的边界条件；再通过微分求积法对控制方程和两类边界条件进行离散；最后通过数值计算分析振动特性．通过改变旋转角速度、轮毂半径、非局部参数以及外部电压分析它们对压电纳米梁振动频率的影响关系．数值结果表明这些参数对压电纳米梁固有频率有不可忽略的影响，本文进一步讨论了旋转角速度对结构模态的影响．     

模拟数字电视信号同缆传输的调试问题

有线数字电视整转过渡期间,模拟、数字电视信号同缆传输将会存在一段时间,如何尽量减少模拟、数字两种电视信号的相互干扰是至关重要的问题,这里包括对机房前端的信号调制、网络传输的技术指标分配、终端接收的信号调节等环节,必须严格执行有关的技术规范。     

基于晶体延迟干涉仪的20-Gb/sNRZ-DQPSK解调实验研究

光差分四相移键控(DQPSK)信号解调技术是相位调制光纤通信系统中的关键技术,本文利用钒酸钇(YVO4)晶体设计制作了2 bit延迟干涉仪(DI)作为DQPSK解调器。相对于传统的基于光纤结构的DI,用晶体材料制作的DI具有温度稳定性高的特点,其作为光DQPSK解调技术中的关键器件,具有广泛的应用前景。实验搭建了20 Gb/s光NRZ-DQPSK背靠背实验系统,并利用自主设计制作的DI成功实现了NRZ-DQPSK信号解调。实验结果与计算机仿真计算结果一致。