Piecewise

About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.

Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation

Abstract: This paper is concerned with computing accurate approximations to the eigenvalues and eigenfunctions of regular Sturm–Liouville differential equations The method consists of replacing the coefficient functions of the given problem by piecewise polynomial functions and then solving the resulting simplified problem Error estimates in terms of the approximate solutions are established and numerical results are displayed Since the asymptotic properties for Sturm–Liouville systems are preserved by the approximation, the relative error in the higher eigenvalues is much more uniform than is the case for finite difference or Rayleigh–Ritz methods

A Dynamic Piecewise Linear Model for DC Transmission Losses in Optimal Scheduling Problems

Abstract: This paper proposes a dynamic piecewise linear model to represent dc transmission losses in optimal scheduling problems. An iterative procedure is proposed, where the linear cuts to approximate quadratic losses in each transmission line are adjusted iteratively as the optimization problem is solved. Applications of this approach to the network constrained short-term hydrothermal scheduling problem and to static dc optimal power flow problems yield a higher accuracy in representing line transmission losses as compared to other approaches, such as a priori iterative estimation, static piecewise liner model and successive linear programming. Study cases for a large-scale system also show reasonable results regarding CPU times.

Higher-order zig-zag model for analysis of thick composite beams with inclusion of transverse normal stress and sublaminates approximations

Abstract: A modified zig-zag technical theory, suitable for the analysis of thick composite beams with rectangular cross section, general lay-up and in cylindrical bending is developed and tested. An equivalent single-layer model and a multiple-layer model are implemented. The displacement field of both these models is postulated as to allow for appropriate jumps in the strains, so that the transverse shear and the transverse normal stress and stress gradient continuity at the interfaces are met. A third-order piecewise approximation for the in-plane displacement and a fourth-order piecewise approximation for the transverse displacement are assumed in the two models. Their predictive capability is investigated in sample cases wherein the exact three-dimensional elasticity and other approximate solutions are available. On the basis of this numerical investigation, they appear to predict accurately and efficiently the displacement and stress fields of composite beams with layers of different materials.