Factorial experiments-Computational procedures and numerical examples.

1962 ◽  
pp. 228-297 ◽  
Author(s):  
B. J. Winer
Keyword(s):  
Factorial Experiments ◽  
Numerical Examples ◽  
Computational Procedures

A Friendly Iterative Technique for Solving Nonlinear Integro-Differential and Systems of Nonlinear Integro-Differential Equations

2018 ◽  
Vol 15 (03) ◽  
pp. 1850016 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Approximate Solution ◽  
Differential Operator ◽  
Differential Equations ◽  
The Other ◽  
Iterative Technique ◽  
Restrictive Assumption ◽  
Numerical Examples ◽  
Linear And Nonlinear ◽  
Computational Procedures ◽  
Adomian’S Polynomials

In this work, a simple new iterative technique based on the integral operator, the inverse of the differential operator in the problem under consideration, is introduced to solve nonlinear integro-differential and systems of nonlinear integro-differential equations (IDEs). The introduced technique is simpler and shorter in its computational procedures and time than the other methods. In addition, it does not require discretization, linearization or any restrictive assumption of any form in providing analytical or approximate solution to linear and nonlinear equations. Also, this technique does not require calculating Adomian’s polynomials, Lagrange’s multiplier values or equating the terms of equal powers of the impeding parameter which need more computational procedures and time. These advantages make it reliable and its efficiency is demonstrated with numerical examples.

Granular Synthesis of Rule-Based Models and Function Approximation Using Rough Sets

2010 ◽  
pp. 408-425 ◽  
Author(s):  
Carlos Pinheiro ◽  
Fernando Gomide ◽  
Otávio Carpinteiro ◽  
Isaías Lima
Keyword(s):  
Nonlinear Systems ◽  
Rough Sets ◽  
Estimation Procedure ◽  
New Method ◽  
Rule Based ◽  
Numerical Examples ◽  
Rule Sets ◽  
Computational Procedures ◽  
Granular Synthesis ◽  
And Function

This chapter suggests a new method to develop rule-based models using concepts about rough sets. The rules encapsulate relations among variables and give a mechanism to link granular descriptions of the models with their computational procedures. An estimation procedure is suggested to compute values from granular representations encoded by rule sets. The method is useful to develop granular models of static and dynamic nonlinear systems and processes. Numerical examples illustrate the main features and the usefulness of the method.

Computational Aspects in the Elasto/Viscoplastic Material Behavior of Solids

2012 ◽  
Vol 567 ◽  
pp. 192-199 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Constitutive Model ◽  
Material Behavior ◽  
Inelastic Behavior ◽  
Viscoplastic Material ◽  
Solid Materials ◽  
Numerical Examples ◽  
Computational Aspects ◽  
Computational Procedures ◽  
Consistent Tangent Operator ◽  
Algorithmic Procedure

In the present paper a computational algorithmic procedure is presented for modeling the elasto/viscoplastic behavior of solid materials. The effects of different loading programs on the inelastic behavior of rate-sensitive materials are analyzed with specific numerical examples. An appropriate solution scheme and a consistent tangent operator are applied which are capable to be adopted for general computational procedures. Numerical computations and results are reported which illustrate the rate-dependence of the constitutive model in use.

Analysis of Queueing Networks in Equilibrium

2020 ◽  
Vol 12 (4) ◽  
pp. 1-17
Author(s):  
Izabella V. Lokshina ◽  
Cees J. M. Lanting
Keyword(s):  
Markov Chains ◽  
Communication Networks ◽  
Queueing Networks ◽  
Numerical Solutions ◽  
Gaussian Elimination ◽  
Steady State Analysis ◽  
Numerical Examples ◽  
Queuing Models ◽  
Stochastic Techniques ◽  
Computational Procedures

Equilibria of queueing networks are a means for performance analysis of real communication networks introduced as Markov chains. In this paper, the authors developed, evaluated, and compared computational procedures to obtain numerical solutions for queueing networks in equilibrium with the use of direct, iterative, and aggregative techniques in steady-state analysis of Markov chains. Advanced computational procedures are developed with the use of Gaussian elimination, power iteration, Courtois' decomposition, and Takahashi's iteration techniques. Numerical examples are provided together with comparative analysis of obtained results. The authors consider these procedures are also applicable to other domains where systems are described with comparable queuing models and stochastic techniques are sufficiently relevant. Several suitable domains of applicability are proposed.

scholarly journals A note on computing the generalized inverseA T,S (2)of a matrixA

2002 ◽  
Vol 31 (8) ◽  
pp. 497-507 ◽  
Author(s):  
Xiezhang Li ◽  
Yimin Wei
Keyword(s):  
Iterative Methods ◽  
Half Plane ◽  
Generalized Inverse ◽  
Null Space ◽  
Drazin Inverse ◽  
Numerical Examples ◽  
Special Cases ◽  
Computational Procedures

The generalized inverseA T,S (2)of a matrixAis a{2}-inverse ofAwith the prescribed rangeTand null spaceS. A representation for the generalized inverseA T,S (2)has been recently developed with the conditionσ (GA| T)⊂(0,∞), whereGis a matrix withR(G)=TandN(G)=S. In this note, we remove the above condition. Three types of iterative methods forA T,S (2)are presented ifσ(GA|T)is a subset of the open right half-plane and they are extensions of existing computational procedures ofA T,S (2), including special cases such as the weighted Moore-Penrose inverseA M,N †and the Drazin inverseAD. Numerical examples are given to illustrate our results.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

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.

Assessing maximal allowable levels for simultaneous skin and eyes exposure to laser irradiation of various wavelengths

2019 ◽  
pp. 35-38
Author(s):  
Boris N. Rakhmanov ◽  
Vladimir I. Kezik ◽  
Vladimir T. Kibovsky ◽  
Valentin M. Ponomarev
Keyword(s):  
Total Energy ◽  
Laser Irradiation ◽  
Customs Union ◽  
Economic Community ◽  
Laser Safety ◽  
Numerical Examples ◽  
Allowable Level ◽  
Correct Formula

Introduction.Evidences prove falseness of formula determining maximal allowable level of total energy of laser irradiation in case when eyes or skin are simultaneously exposed to several irradiation sources with various wavelengths. The formula was mentioned in actual «Sanitary rules and regulations for lasers construction and exploitation» Nо 5804–91 and in SanPiN 2.2.4.3359–16, that in a part of VIII section «Laser irradiation atworkplace» are latest acting regulation document on laser safety. SanPiN 2.2.4.13–2–2006 of Belarus Republic and regulation document Nо 299 of Customs Union Commission of Eurasia Economic Community on 28/05/2010 appeared to contain other, more correct formula determining the same maximal allowable level.Objectivewas to improve regulation basis in laser safety by correcting mistakes made previously in regulation documents.Deducing formulae.The article presents thorough and consistent deducing a formula to determine total energy of laser irradiation in case when eyes or skin are simultaneously and jointly exposed to several irradiation sources with various wavelengths. The efforts resulted in the formula that agreed with formulae presented in the regulation document on laser safety of Belarus Republic and in the regulation document Nо 299 of Customs Union Commission of Eurasia Economic Community on 28/05/2010.Discussion.Correctness of the obtained formula is supported by numerical examples and by comparison with other formulae used in regulation documents on hygienic regulation of other acting factors.Conclusion.Results of the work are summarized, and emphasis is made on its value for solving problems of improving regulation basis for laser safety.

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