scholarly journals Extended Convergence Analysis of the Newton–Hermitian and Skew–Hermitian Splitting Method

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 981
Author(s):  
Ioannis K Argyros ◽  
Santhosh George ◽  
Chandhini Godavarma ◽  
Alberto A Magreñán
Keyword(s):  
Applied Mathematics ◽  
Splitting Method ◽  
Convergence Criterion ◽  
System Of Nonlinear Equations ◽  
Recurrent Functions ◽  
Numerical Examples ◽  
Convection Diffusion ◽  
The One ◽  
The Given ◽  
Theoretical Results

Many problems in diverse disciplines such as applied mathematics, mathematical biology, chemistry, economics, and engineering, to mention a few, reduce to solving a nonlinear equation or a system of nonlinear equations. Then various iterative methods are considered to generate a sequence of approximations converging to a solution of such problems. The goal of this article is two-fold: On the one hand, we present a correct convergence criterion for Newton–Hermitian splitting (NHSS) method under the Kantorovich theory, since the criterion given in Numer. Linear Algebra Appl., 2011, 18, 299–315 is not correct. Indeed, the radius of convergence cannot be defined under the given criterion, since the discriminant of the quadratic polynomial from which this radius is derived is negative (See Remark 1 and the conclusions of the present article for more details). On the other hand, we have extended the corrected convergence criterion using our idea of recurrent functions. Numerical examples involving convection–diffusion equations further validate the theoretical results.

scholarly journals Competitive Analysis for Online Leasing Problem with Compound Interest Rate

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Xingyu Yang ◽  
Weiguo Zhang ◽  
Weijun Xu ◽  
Yong Zhang
Keyword(s):  
Interest Rate ◽  
Competitive Analysis ◽  
The Other ◽  
Continuous Version ◽  
Numerical Examples ◽  
The Interest Rate ◽  
The One ◽  
Compound Interest ◽  
Theoretical Results ◽  
Deterministic Strategy

We introduce the compound interest rate into the continuous version of the online leasing problem and discuss the generalized model by competitive analysis. On the one hand, the optimal deterministic strategy and its competitive ratio are obtained; on the other hand, a nearly optimal randomized strategy is constructed and a lower bound for the randomized competitive ratios is proved by Yao's principle. With the help of numerical examples, the theoretical results show that the interest rate puts off the purchase date and diminishes the uncertainty involved in the decision making.

scholarly journals A Semilocal Convergence for a Uniparametric Family of Efficient Secant-Like Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
I. K. Argyros ◽  
D. González ◽  
Á. A. Magreñán
Keyword(s):  
Banach Space ◽  
Computational Cost ◽  
Semilocal Convergence ◽  
Recurrent Functions ◽  
Convergence Conditions ◽  
Precise Information ◽  
Numerical Examples ◽  
Convergence Results ◽  
Special Cases ◽  
Theoretical Results

We present a semilocal convergence analysis for a uniparametric family of efficient secant-like methods (including the secant and Kurchatov method as special cases) in a Banach space setting (Ezquerro et al., 2000–2012). Using our idea of recurrent functions and tighter majorizing sequences, we provide convergence results under the same or less computational cost than the ones of Ezquerro et al., (2013, 2010, and 2012) and Hernández et al., (2000, 2005, and 2002) and with the following advantages: weaker sufficient convergence conditions, tighter error estimates on the distances involved, and at least as precise information on the location of the solution. Numerical examples validating our theoretical results are also provided in this study.

scholarly journals Well-posedness and numerical approximation of tempered fractional terminal value problems

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Maria Luísa Morgado ◽  
Magda Rebelo
Keyword(s):  
Numerical Methods ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Numerical Approximation ◽  
Shooting Method ◽  
Well Posedness ◽  
Numerical Examples ◽  
Uniqueness Of The Solution ◽  
The Given ◽  
Theoretical Results

AbstractFor a class of tempered fractional terminal value problems of the Caputo type, we study the existence and uniqueness of the solution, analyze the continuous dependence on the given data, and using a shooting method we present and discuss three numerical schemes for the numerical approximation of such problems. Some numerical examples are considered in order to illustrate the theoretical results and evidence the efficiency of the numerical methods.

THE EU SUGAR MARKET PROFILE AND ITS MAIN DRIVERS

2015 ◽  
Author(s):  
Lubos SMUTKA ◽  
Irena BENEŠOVÁ ◽  
Patrik ROVNÝ ◽  
Renata MATYSIK-PEJAS
Keyword(s):  
Market Failure ◽  
Current System ◽  
Quota System ◽  
Considerable Debate ◽  
Sugar Market ◽  
The Common ◽  
The One ◽  
Production Capacities ◽  
The Given ◽  
The Eu

Sugar is one of the most important elements in human nutrition. The Common Market Organisation for sugar has been a subject of considerable debate since its establishment in 1968. The European agricultural market has been criticized for its heavy regulations and subsidization. The sugar market is one of the most regulated ones; however, this will change radically in 2017 when the current system of production quotas will end. The current EU sugar market changed is structure during the last several decades. The significant number of companies left the market and EU internal sugar market became more concentrated. The aim of this paper is presentation characteristics of sugar market with respect to the supposed market failure – reduction in competition. The analysis also identifies the main drivers and determinants of the EU especially quota sugar market. In relation to paper’s aim the following results are important. The present conditions of the European sugar market have led to market failure when nearly 75 % (10 million tonnes) of the quota is controlled by five multinational companies only. These multinational alliances (especially German and French one) are also taking control over the production capacities of their subsidiaries. In most countries, this causes serious problems as the given quota is controlled by one or two producers only. This is a significant indicator of market imperfection. The quota system cannot overcome the problem of production quotas on the one hand and the demand on the other; furthermore, it also leads to economic inefficiency. The current EU sugar market is under the control of only Sudzucker, Nordzucker, Pfeifer and Langen, Tereos and ABF.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

Quasi-Periodic Control Technique for Minimizing Fuel Consumption During Record Vehicle Competition

2013 ◽  
Vol 60 (2) ◽  
pp. 185-197 ◽  
Author(s):  
Paweł Sulikowski ◽  
Ryszard Maronski
Keyword(s):  
Fuel Consumption ◽  
Optimal Control Theory ◽  
Slope Angle ◽  
Control Technique ◽  
Decision Variables ◽  
Aeronautical Engineering ◽  
The One ◽  
Optimal Driving ◽  
The Given ◽  
Engine Power

The problem of the optimal driving technique during the fuel economy competition is reconsidered. The vehicle is regarded as a particle moving on a trace with a variable slope angle. The fuel consumption is minimized as the vehicle covers the given distance in a given time. It is assumed that the run consists of two recurrent phases: acceleration with a full available engine power and coasting down with the engine turned off. The most fuel-efficient technique for shifting gears during acceleration is found. The decision variables are: the vehicle velocities at which the gears should be shifted, on the one hand, and the vehicle velocities when the engine should be turned on and off, on the other hand. For the data of students’ vehicle representing the Faculty of Power and Aeronautical Engineering it has been found that such driving strategy is more effective in comparison with a constant speed strategy with the engine partly throttled, as well as a strategy resulting from optimal control theory when the engine is still active.

scholarly journals An Existence Theory for Gravity–Capillary Solitary Water Waves

Water Waves ◽  
2021 ◽  
Author(s):  
M. D. Groves
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Applied Mathematics ◽  
Spatial Dynamics ◽  
Existence Theory ◽  
Water Wave Problem ◽  
Reduction Methods ◽  
Centre Manifold Reduction ◽  
Weak Surface ◽  
The One

AbstractIn the applied mathematics literature solitary gravity–capillary water waves are modelled by approximating the standard governing equations for water waves by a Korteweg-de Vries equation (for strong surface tension) or a nonlinear Schrödinger equation (for weak surface tension). These formal arguments have been justified by sophisticated techniques such as spatial dynamics and centre-manifold reduction methods on the one hand and variational methods on the other. This article presents a complete, self-contained account of an alternative, simpler approach in which one works directly with the Zakharov–Craig–Sulem formulation of the water-wave problem and uses only rudimentary fixed-point arguments and Fourier analysis.

scholarly journals Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

2021 ◽  
Author(s):  
Radu Boţ ◽  
Guozhi Dong ◽  
Peter Elbau ◽  
Otmar Scherzer
Keyword(s):  
Linear Operator ◽  
Operator Equation ◽  
Convex Analysis ◽  
Convergence Rates ◽  
Linear Operator Equation ◽  
Optimal Convergence Rates ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Given ◽  
Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

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