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91.
J.M. Melenk 《Journal of Computational and Applied Mathematics》2010,234(6):1692-1701
We analyze the convergence behavior of Filon-type quadrature rules by making explicit the dependence on both k, the parameter that controls the oscillatory behavior of the integrand, and n, the number of function evaluations. We provide explicit conditions on the domain of analyticity of the integrand to ensure convergence for n→∞. 相似文献
92.
史琬琰 《河海大学学报(自然科学版)》1989,17(1):45-49
本文研究了在应用中颇为重要的几类非线性偏微分方程的振荡解。首先,我们讨论了修正KdV方程、二维KdV方程和Boussinesq方程,利用Jacobl椭圆函数作出了这些方程转化后的常微分方程的解,从而证明了原方程行波振荡解的存在性。其次,我们研究了高维约比波动方程。对所归结的微分方程构造了它的一个幂级数解,导出了此解与Bessel函数的关系,然后由Bessel函数的实零点的分布结果证明了高维约化波动方程的柱面振荡解的存在性。 相似文献
93.
王宏伟 《新乡学院学报(自然科学版)》2012,(5):387-388
利用Fourier 限制算子和一个振荡积分不等式,得出了线性 Rosenau 方程解的高频部分的时空估计. 相似文献
94.
Yinhu Xi Yuan Zhou Wei Zhang Junhong Mao 《科学通报(英文版)》2014,(29):3912-3918
Friction behaviors of linear rolling guides (LRGs) are determined by many factors and are crucial for precision positioning. It is difficult to create an expression to describe the friction behaviors exactly and completely. A new experimental method for measuring the friction behaviors of one LRG individually was developed, and linear motor direct drive technology is utilized in the experiment setup. The position signal is acquired by a grating, and the friction of the LRG is deduced by the product of the mass of the moving part and its acceleration. In the experiment, the LRG can move with the friction only, and the friction transition from normal rolling to pre- rolling stage was detected. The asperities' deformations were utilized to explain it. Hysteresis loops and internal loops were measured. The results indicate the non-local memory of the LRG, and the historical trajectory have an important impact on the friction behaviors of LRGs in the pre-rolling stage. 相似文献
95.
M. Khanamiryan 《BIT Numerical Mathematics》2008,48(4):743-761
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 相似文献
96.
Huoxiong Wu 《逼近论及其应用》2009,(3):230-241
In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 〈 p 〈 ∞, the L^p-boundedness of such operators are obtained provided that their kernels belong to the spaces L^q(s^n-1) for some q 〉 1. 相似文献
97.
We consider the approximation of trigonometric operator functions that arise in the numerical solution of wave equations by
trigonometric integrators. It is well known that Krylov subspace methods for matrix functions without exponential decay show
superlinear convergence behavior if the number of steps is larger than the norm of the operator. Thus, Krylov approximations
may fail to converge for unbounded operators. In this paper, we propose and analyze a rational Krylov subspace method which
converges not only for finite element or finite difference approximations to differential operators but even for abstract,
unbounded operators. In contrast to standard Krylov methods, the convergence will be independent of the norm of the operator
and thus of its spatial discretization. We will discuss efficient implementations for finite element discretizations and illustrate
our analysis with numerical experiments.
AMS subject classification (2000) 65F10, 65L60, 65M60, 65N22 相似文献
98.
The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with
highly oscillatory solutions is studied in this paper. The numerical methods considered are symmetric trigonometric integrators
and the St?rmer–Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency
case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results
are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system.
A brief discussion of conservation properties in the continuous problem is also included.
AMS subject classification (2000) 65L05, 65P10 相似文献
99.
A class of multilinear oscillatory singular integrals with smooth phases is studied. And their uniform boundedness on Lebesgue space is proved. 相似文献
100.
In this paper, we study monopolistic pricing behaviors within a two-way network. In this symbiotic production system, independent decision centers carry out an activity which concurs to the production of different system goods. The players are assumed to know the whole network. Due to this rationality, they try to capture a share of the profit of the firms who sell the system goods to the consumers. These double marginalization behaviors are studied within very general networks. Conditions with ensure existence and uniqueness are discussed. We even provided a complete characterization of an equilibrium. Potential applications are also discussed 相似文献