A general framework for proving an order of convergence for set-valued Runge Kutta methods is given in the case of linear differential inclusions, if the attainable set at a given time should be approximated. The set-valued method is interpreted as a (set-valued) quadrature method with disturbed values for the fundamental solution at the nodes of the quadrature method. If the precision of the q...

Highly-oscillatory integrals are allegedly difficult to calculate. The main assertion of this paper is that that impression is incorrect. As long as appropriate quadrature methods are used, their accuracy increases when oscillation becomes faster and suitable choice of quadrature points renders this welcome phenomenon more pronounced. We focus our analysis on Filon-type quadrature and analyse i...

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 f...

This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes. AMS Subject Classfication: 65D30, 65D32, 65N38.

A simple method which is rigorously invariant under molecular rotations is presented for evaluation of the density functional exchange-correlation energy by numerical quadrature. The corresponding expressions for the first and second derivatives of the energy with respect to nuclear displacement are presented. In particular, such a scheme is necessary to remove the difficulties previously encou...

Using 1-μm InP HBT technology, a transimpedance amplifier (TIA) IC for optical links using 100-Gb/s dual polarization quadrature phase shift keying (100-G DP-QPSK) was designed and fabricated. Its wide dynamic range of 0.2∼2mAppd input current and good linearity of less than 3.3-% total harmonic distortion (THD) were confirmed. Also, externally controllable functions such as output amplitude ad...

In this workwe propose and analyze a fully discretemodifiedCrank–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 c...

ˇThe effect of the non-linear interaction between the high density Wannier excitons is analysed. We use the Fokker-Planck equation in the positive P presentation and the corresponding stochastic differential equation to study the composite system of a single mode cavity field and exciton under classical field pumping. The small fluctuation approximation is made to get the quadrature squeezing s...

The two-harmonic FD-OCT method, where the quadrature components of the spectral interferogram are obtained by simultaneous acquisition of the first and second harmonics of the phase-modulated interferogram, is used for complexconjugate-resolved imaging of biological samples. The method is implemented using sampling of the phase modulated interferogram with an integrating detector array followed...