VALUES OF SOME EXPRESSIONS WHICH ARE PRESENTED UNDER THE INDETERMINATE FORM $$\frac{\infty }{\infty }, \infty ^{0}, \, \dots .$$   A RELATIONSHIP WHICH EXISTS BETWEEN THE RATIO OF FINITE DIFFERENCES AND THE DERIVED FUNCTION.

2019 ◽  
pp. 31-35
Author(s):  
Dennis M. Cates
Keyword(s):  
Finite Differences ◽  
Indeterminate Form ◽  
Derived Function

THE METHOD OF FINITE DIFFERENCES APPLIED TO DESCRIPITION OF A METALIC COMPONENT

2017 ◽  
Author(s):  
Lisiane Trevisan ◽  
Juliane Donadel ◽  
Bianca de Castro
Keyword(s):  
Finite Differences

Finite differences with exponential filtering in the calculation of reactivity

Kerntechnik ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. 210-213 ◽  
Author(s):  
D. Suescún Díaz ◽  
A. Senra Martinez
Keyword(s):  
Finite Differences

Umbral Calculus

10.37236/24 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
A. Di Bucchianico ◽  
D. Loeb
Keyword(s):  
19Th Century ◽  
Finite Differences ◽  
State Of The Art ◽  
Umbral Calculus ◽  
Current State ◽  
Logical Foundation ◽  
Complete Bibliography ◽  
The 19Th Century ◽  
Mathematical Literature

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly.

Solving the Korteweg-de Vries equation with Hermite-based finite differences

2021 ◽  
Vol 401 ◽  
pp. 126101
Author(s):  
Dylan Abrahamsen ◽  
Bengt Fornberg
Keyword(s):  
Finite Differences ◽  
Vries Equation ◽  
De Vries

scholarly journals The Turbulent Flow over the BARC Rectangular Cylinder: A DNS Study

2021 ◽  
Author(s):  
Alessandro Chiarini ◽  
Maurizio Quadrio
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Finite Differences ◽  
Turbulence Models ◽  
Fine Tuning ◽  
Rectangular Cylinder ◽  
Budget Equation ◽  
Complete Set ◽  
First Time

AbstractA direct numerical simulation (DNS) of the incompressible flow around a rectangular cylinder with chord-to-thickness ratio 5:1 (also known as the BARC benchmark) is presented. The work replicates the first DNS of this kind recently presented by Cimarelli et al. (J Wind Eng Ind Aerodyn 174:39–495, 2018), and intends to contribute to a solid numerical benchmark, albeit at a relatively low value of the Reynolds number. The study differentiates from previous work by using an in-house finite-differences solver instead of the finite-volumes toolbox OpenFOAM, and by employing finer spatial discretization and longer temporal average. The main features of the flow are described, and quantitative differences with the existing results are highlighted. The complete set of terms appearing in the budget equation for the components of the Reynolds stress tensor is provided for the first time. The different regions of the flow where production, redistribution and dissipation of each component take place are identified, and the anisotropic and inhomogeneous nature of the flow is discussed. Such information is valuable for the verification and fine-tuning of turbulence models in this complex separating and reattaching flow.

Marine Pipeline Analysis Based on Newton’s Method With an Arctic Application

1970 ◽  
Vol 92 (4) ◽  
pp. 827-833 ◽  
Author(s):  
D. W. Dareing ◽  
R. F. Neathery
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Newton’S Method ◽  
Finite Differences ◽  
Newton's Method ◽  
Nonlinear Differential Equations ◽  
Bending Moments ◽  
Iterative Solutions ◽  
Linear Differential ◽  
Pipe Deflection

Newton’s method is used to solve the nonlinear differential equations of bending for marine pipelines suspended between a lay-barge and the ocean floor. Newton’s method leads to linear differential equations, which are expressed in terms of finite differences and solved numerically. The success of Newton’s method depends on initial trial solutions, which in this paper are catenaries. Iterative solutions converge rapidly toward the exact solution (pipe deflection) even though large bending moments exist in the pipe. Example calculations are given for a 48-in. pipeline suspended in 300 ft of water.

Derivative-dependent control of a fuel cell system with a safe implementation: An artificial delay approach

2021 ◽  
pp. 095965182110127
Author(s):  
Adrián Ramírez ◽  
Rifat Sipahi ◽  
César-Fernando Mendéz-Barrios ◽  
Jesús Leyva-Ramos
Keyword(s):  
Fuel Cell ◽  
Finite Differences ◽  
Clean Energy ◽  
Cell System ◽  
Fuel Cell System ◽  
Safe Operation ◽  
Control Activity ◽  
Renewable Energy Systems ◽  
Control Scheme ◽  
Unknown Disturbances

The growing demand for energy in recent decades has been followed by an increasing interest in clean energy sources as means to mitigate environmental pollution. Accordingly, renewable energy systems are required to not only guarantee safe operation but also have the ability to regulate their responses dynamically against operational variations and disturbances. Here, we propose a derivative-dependent controller to optimize this dynamic response in a fuel cell system. Since derivatives are in general difficult to measure or construct reliably, it is common practice to approximate them using finite-differences. This approximation, if not performed carefully, may produce undesired control activity and even instability. In this article, we propose to systematically engineer the finite-differences using artificial delays so as to avoid those undesired outcomes. This therefore guarantees a safe implementation of the control scheme. The objective of the proposed controller is to regulate the fuel cell’s output voltage while quickly compensating for parametric variations and unknown disturbances without the need of explicitly measuring or estimating them. Simulation results verify the advantages of the approach demonstrating that the controller with artificial delays is a preferable substitute for ideal derivative-dependent control implementations in fuel cell applications.

scholarly journals The Mimetic Methods Toolkit: An object-oriented API for Mimetic Finite Differences

2014 ◽  
Vol 270 ◽  
pp. 308-322 ◽  
Author(s):  
Eduardo J. Sanchez ◽  
Christopher P. Paolini ◽  
Jose E. Castillo
Keyword(s):  
Finite Differences ◽  
Object Oriented ◽  
Mimetic Finite Differences
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