Existence,Uniqueness and Applications of the Spline Method for Functional-Differential Equation of Neutral Type

This paper presents a class of numerical method for the approximate solution for the functional-differential equation of neutral type. These methods are essentially based on the spline functions. The study of existence and uniqueness are considered of 3h-step spline function of degree m =4. Numerical examples and comparisons with other methods are given.     

Convergence of the spline function for functional-differential equation of neutral type

The existence, uniqueness and stability for the functional-differential equation of neutral type using spline of deficiency 3 with stepsize 3h spline function of degree four are presented in Ref. [1]. In this paper, we extend the study to the convergence of our proposed spline method. We prove that, if the local error is of order p, then the global error is of order p as well. Numerical examples are presented to illustrate the convergence of the method.     

Stability and convergence of the two parameter cubic spline collocation method for delay differential equations

In this paper, we propose the cubic spline collocation method with two parameters for solving delay differential equations (DDEs). Some results of the local truncation error and the convergence of the spline collocation method are given. We also obtain some results of the linear stability and the nonlinear stability of the method for DDEs. In particular, we design an algorithm to obtain the ranges of the two parameters α,β which are necessary for the P-stability of the collocation method. Some illustrative examples successfully verify our theoretical results.     

Numerical solution of system of first-order delay differential equations using polynomial spline functions

The use of two constructed polynomial spline functions to approximate the solution of a system of first-order delay differential equations is described. The first spline function is a polynomial with an undetermined constant coefficient in the last term. The other has a polynomial spline form. The error analysis and stability of the second function are theoretically investigated and a test example is given. A comparison of the two forms is carried out to illustrate the pertinent features of the proposed techniques.     

GP-Stability of two-step implicit runge-kutta methods for delay differential equations

The GP-stability of two-step implicit Runge-Kutta (TIRK) methods for the numerical solution of systems of delay differential equations (DDEs) is considered. We focus on the stability behaviour of TIRK methods in the solution of the linear constant-coefficient systems of DDE with a single delay. We present a sufficient condition of GP-stability of TIRK methods.     

Existence and uniqueness of mild solutions for abstract delay fractional differential equations

In this paper, by means of solution operator approach and contraction mapping theorem, the existence and uniqueness of mild solutions for a class of abstract delay fractional differential equations are obtained.     

Existence, uniqueness and stability of the equilibrium points of a SHARON bioreactor model

This paper addresses the dynamics of a SHARON reactor, a promising technology for ammonium removal from concentrated wastewater streams. The contraction mapping theorem is used to determine which operating conditions of a SHARON reactor with pH-control result in a unique equilibrium state. However, this approach only identifies the case of very large dilution rates, in practice corresponding with complete biomass wash-out, i.e. with complete loss of biological activity. Practical operation of a SHARON reactor aims at reaching ammonium conversion to nitrite. To identify such interesting operating points, the equilibrium points are subsequently calculated directly in terms of input variables for a simplified SHARON reactor model. The stability of the obtained equilibrium points is assessed and the corresponding phase portraits are analyzed. The influence of slightly varying parameter and input values is investigated as well.     

EIQNK curve analysis for the design of distribution center and warehouse with spline function

This paper discussed the EIQ and EIQNK curve metohd for the selection of machine and equipments in the design of distribution center or warehouse.This curve are expressed with orthogonal polynominals and spline functions and how the function applied of this problems.The shape of EIQNK curves are split into differents classes and discussed the characteristic of warehouse or distribution. Fuzzy EIQNK curve analysis also discussed.     

Robust stability of dynamic predictor based control laws for input and state delay systems

The robust stability properties of the dynamic predictor scheme for state and input delay systems are analyzed in the frequency domain. Robust stability bounds are presented for the cases of uncertainty of the matrix parameters, of the state or input delay, and of the combination of both. An example illustrates the results.     

Parallel Difference Schemes For Heat Conduction Equations * The work is supported by the Chinese National Key Program for Developing Basic Science,G1999032801, the National Natural Science Foundation of China (19932010) and the Foundation of CAEP (2X0107)

In this paper a parallel difference scheme based on Dufort-Frankel scheme and the classic implicit scheme for linear heat conduction equations is studied. In this procedure, the values at subdomain interfaces are calculated by using the Dufort-Frankel scheme, and then these values serve as Dirichlet boundary data for the implicit scheme in the subdomains. The weak necessary condition of the unconditional stability of the parallel difference scheme is proved. Numerical experiments indicates that the parallel difference scheme has good parallelism, and has better accuracy than the fully implicit scheme.     

A hybrid approach for optimal location and capacity of UPFC to improve the dynamic stability of the power system

In this document, the Firefly Algorithm (FA) and Cuckoo Search (CS) algorithm based on optimal location and the capacity of UPFC to improve the dynamic stability of the power system are proposed. The novelty of the proposed method is exemplified in the improved searching ability, random reduction and reduced complexity. In this regard, the generator fault affects the system dynamic stability constraints such as voltage, power loss, real and reactive power. Here, the FA technique optimizes the maximum power loss line as the suitable location of the UPFC. The affected location parameters and dynamic stability constraints are restored into secure limits using the optimum capacity of the UPFC, which in turn, has been optimized with reduced cost by using the CS algorithm. The attained capacity of the UPFC has been located in the affected location and the power flow of the system analyzed. The proposed method is implemented in the MATLAB/Simulink platform and tested under IEEE 30 and IEEE 14 standard bench mark system. The proposed method performance is evaluated by comparison with those of different techniques such as ABC-GSA, GSA-Bat, Bat-FA and CS algorithms. The comparison results invariably prove the effectiveness of the proposed method and confirm its potential to solve the related problems.     

Roadmap for the next generation of dynamic function allocation theories and strategies

Dynamic function allocation theories have matured, but not to the extent that they can be implemented in actual environments. The authors identify a roadmap to help to get to that stage, after a brief review of relevant function allocation theories and the gaps in knowledge in adaptive allocation theories. Past research has focused on short‐term implementations of dynamic function allocation, which last for minutes (but never more than a few hours). Stable and enduring implementations of dynamic function allocation, lasting over days or possibly years, require a better and scientific understanding of the interaction among trigger mechanisms, adaptation strategies, and interruption strategies. The possibility of an unintentional consequence of this adaptive allocation, that the automated agent becomes confined to limited levels of automation, has to be ruled out after experimental evidence. © 2010 Wiley Periodicals, Inc.     

Development of a software tool for rapid,reproducible, and stakeholder-friendly dynamic coupling of system dynamics and physically-based models

System Dynamics (SD) modeling is well adapted to developing participatory environmental models. However, SD models are ill-suited for complex physical (e.g., groundwater) processes, and existing methods to couple them with physically-based models tend to be complex and inflexible. We here present Tinamit, a novel tool to couple SD and physically-based models in a rapid, reproducible, and stakeholder-friendly manner. Tinamit requires only a few lines of Python code to couple and simulate models (or, with its interface, no coding at all), which is expected to make model coupling more accessible to stakeholders and allow them to continue developing coupled models after the end of a funded project. We use Tinamit to couple a SD-based farmer economics model from Pakistan with a soil salinity model (SAHYSMOD) and analyze the trade-offs of various policies, of which canal lining with subsidies seemed promising. Such results cannot be readily obtained from either model alone.     

Biotechnical measurement and software system controlled features for determining the level of psycho-emotional tension on man-machine systems by fuzzy measures

A new software technique for determining emotional tension on humans is developed by means of psychological tests connected with the psycho-emotional sphere and on indicators characterizing the state of a subject’s visual attention. Each of these two areas determines several factors for psycho-emotional tension. The level of tension is determined as an aggregate of these two components with the rules of fuzzy logic. The membership functions and solving rules for the psychological tests, and for the state of visual attention, are constructed using fuzzy logic theory. It is shown that the resulting method can be used as an informative feature for prediction of many properties, such as the situational awareness (training and experience) of an operator and the operator’s individual capacity to function (mental-physiological limits). The second group of indicators characterize properties such as switchable attention (the ability to switch attention) (SWA), concentration (ability to concentrate) (CNA), stability of visual attention (STA) and parameters determining the state of memory. One of the most important issues for man-machine systems is to evaluate the performance of operators under abnormal conditions such as stress or tension.