The equivalent, second equivalent and (simply) modi®ed equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coecients, they are also equivalent to the original ®nite di€erence scheme. Straightforw...

Abstract In engineering practice, a constant voltage output control system of synchronous rectifier primary side regulator (PSR) flyback converter is proposed to overcome the sampling defect existing digital approximation double line scheme for structure. Regardless slope waveform and knee point, single-output DAC midpoint can achieve high accuracy good point following effect. At same time, neu...

The concept of midpoint percolation has recently been applied to characterize the double percolation transitions in negatively curved structures. Regular d-dimensional hypercubic lattices are investigated in the present work using the same concept. Specifically, the site-percolation transitions at the critical thresholds are investigated for dimensions up to d=10 by means of the Leath algorithm...

in this paper, the non-linear dynamic response of novel steel sandwich panel with hollow i-core subjected to blast loading was studied. special emphasis is placed on the evaluation of midpoint displacements and energy dissipation of the models. several parameters such as boundary conditions, strain rate, mesh dependency and asymmetrical loading are considered in this study. the material and geo...

STUDY DESIGN This was an interventional human cadaver study and radiological study. OBJECTIVES Atlas instrumentation is frequently involved in fusion procedures involving the craniocervical junction area. Identification of the entry point at the center of atlas lateral mass (ALM) is challenging because of its rounded posterior surface and the surrounding venous plexus. This report examines us...

Define an “augmented precision” algorithm as an algorithm that returns, in precision-p floating-point arithmetic, its result as the unevaluated sum of two floatingpoint numbers, with a relative error of the order of 2−2p. Assuming an FMA instruction is available, we perform a tight error analysis of an augmented precision algorithm for the square root, and introduce two slightly different augme...

An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...