Computational solution of fractional pantograph equation with varying $\mathscr{D}$elay term

2021 ◽  
Vol 6 (2) ◽  
pp. 121-145
Author(s):  
M. Khalid ◽  
S. K. Fareeha ◽  
S. Mariam
Keyword(s):  
Pantograph Equation ◽  
Computational Solution

scholarly journals Asymptotic Stability of Nonlinear Discrete Fractional Pantograph Equations with Non-Local Initial Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 473
Author(s):  
Jehad Alzabut ◽  
A. George Maria Selvam ◽  
Rami Ahmad El-Nabulsi ◽  
D. Vignesh ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theorems ◽  
Initial Conditions ◽  
Current Collector ◽  
Stability Of Solutions ◽  
Electric Bus ◽  
Pantograph Equation ◽  
Non Local

Pantograph, the technological successor of trolley poles, is an overhead current collector of electric bus, electric trains, and trams. In this work, we consider the discrete fractional pantograph equation of the form Δ*β[k](t)=wt+β,k(t+β),k(λ(t+β)), with condition k(0)=p[k] for t∈N1−β, 0<β≤1, λ∈(0,1) and investigate the properties of asymptotic stability of solutions. We will prove the main results by the aid of Krasnoselskii’s and generalized Banach fixed point theorems. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

New computational solution to quantify synthetic material porosity from optical microscopic images

2010 ◽  
Vol 240 (1) ◽  
pp. 50-59 ◽  
Author(s):  
V.H.C. DE ALBUQUERQUE ◽  
P.P. REBOUÇAS FILHO ◽  
T.S. CAVALCANTE ◽  
J.M.R.S. TAVARES
Keyword(s):  
Synthetic Material ◽  
Microscopic Images ◽  
Material Porosity ◽  
Computational Solution

Optimizing Cash Management for Large Scale Bank Operations

2010 ◽  
Vol 1 (2) ◽  
pp. 17-31
Author(s):  
Mark Frost ◽  
Jeff Kennington ◽  
Anusha Madhavan
Keyword(s):  
Federal Reserve ◽  
Large Scale ◽  
Programming Model ◽  
Cash Management ◽  
Cost Component ◽  
Time Space ◽  
Currency Management ◽  
The Cost ◽  
Reserve System ◽  
Computational Solution

The Federal Reserve System (Fed) provides currency services to banks, including sorting currency into fit and non-fit bills and repackaging bills for redistribution. To reduce the cost of currency management operations, many banks make Fed deposits and withdrawals of the same denomination each week. In July 2007, the Fed introduced fees for making both deposits and withdrawals during a given Monday through Friday. Recognizing an opportunity, Fiserv Corporation initiated a project to optimize bank vault inventories across time and space. This article presents the integer programming model developed to assist Fiserv clients reduce the logistics cost component of cash management. The model is implemented in software using OPL. The underlying configuration is a time-space multi-commodity network with a fixed-charge cost structure. The authors report on a successful pilot study and present an efficient heuristic procedure that can be used to reduce computational solution times from hours to a few minutes.

A computational solution to analyze hydrophobic characteristics in protein chains

2016 ◽  
Author(s):  
Marilia Amável Gomes Soares ◽  
Alexandre Azevedo ◽  
Sotiris Missailidis ◽  
Dilson Silva
Keyword(s):  
Computational Solution

scholarly journals Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
M. Mustafa Bahşi ◽  
Mehmet Çevik
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Taylor Series Expansion ◽  
Perturbation Parameter ◽  
Iteration Algorithm ◽  
Proportional Delay ◽  
Pantograph Equation ◽  
Functional Differential ◽  
Delay Differential

The pantograph equation is a special type of functional differential equations with proportional delay. The present study introduces a compound technique incorporating the perturbation method with an iteration algorithm to solve numerically the delay differential equations of pantograph type. We put forward two types of algorithms, depending upon the order of derivatives in the Taylor series expansion. The crucial convenience of this method when compared with other perturbation methods is that this method does not require a small perturbation parameter. Furthermore, a relatively fast convergence of the iterations to the exact solutions and more accurate results can be achieved. Several illustrative examples are given to demonstrate the efficiency and reliability of the technique, even for nonlinear cases.

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