Search results for: Chebyshev approximation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 412

Search results for: Chebyshev approximation

262 Contaminant Transport in Soil from a Point Source

Authors: S. A. Nta, M. J. Ayotamuno, A. H. Igoni, R. N. Okparanma

Abstract:

The work sought to understand the pattern of movement of contaminant from a continuous point source through soil. The soil used was sandy-loam in texture. The contaminant used was municipal solid waste landfill leachate, introduced as a point source through an entry point located at the center of top layer of the soil tank. Analyses were conducted after maturity periods of 50 and 80 days. The maximum change in chemical concentration was observed on soil samples at a radial distance of 0.25 m. Finite element approximation based model was used to assess the future prediction, management and remediation in the polluted area. The actual field data collected for the case study were used to calibrate the modeling and thus simulated the flow pattern of the pollutants through soil. MATLAB R2015a was used to visualize the flow of pollutant through the soil. Dispersion coefficient at 0.25 and 0.50 m radial distance from the point of application of leachate shows a measure of the spreading of a flowing leachate due to the nature of the soil medium, with its interconnected channels distributed at random in all directions. Surface plots of metals on soil after maturity period of 80 days shows a functional relationship between a designated dependent variable (Y), and two independent variables (X and Z). Comparison of measured and predicted profile transport along the depth after 50 and 80 days of leachate application and end of the experiment shows that there were no much difference between the predicted and measured concentrations as they were all lying close to each other. For the analysis of contaminant transport, finite difference approximation based model was very effective in assessing the future prediction, management and remediation in the polluted area. The experiment gave insight into the most likely pattern of movement of contaminant as a result of continuous percolations of the leachate on soil. This is important for contaminant movement prediction and subsequent remediation of such soils.

Keywords: Contaminant, dispersion, point or leaky source, surface plot, soil.

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261 Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

Authors: M. Zarebnia, N. Aliniya

Abstract:

In this paper, a numerical solution based on sinc functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Sinc functions; Galerkin; Numerical method

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260 An Approximation Method for Three Quark Systems in the Hyper-Spherical Approach

Authors: B. Rezaei, G. R. Boroun, M. Abdolmaleki

Abstract:

The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

Keywords: Adiabatic expansion, grand angular momentum, binding energy, perturbation, baryons.

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259 Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations

Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati

Abstract:

In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Non-polynomial spline functions; Numerical method

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258 Numerical Approximation to the Performance of CUSUM Charts for EMA (1) Process

Authors: K. Petcharat, Y. Areepong, S. Sukparungsri, G. Mititelu

Abstract:

These paper, we approximate the average run length (ARL) for CUSUM chart when observation are an exponential first order moving average sequence (EMA1). We used Gauss-Legendre numerical scheme for integral equations (IE) method for approximate ARL0 and ARL1, where ARL in control and out of control, respectively. We compared the results from IE method and exact solution such that the two methods perform good agreement.

Keywords: Cumulative Sum Chart, Moving Average Observation, Average Run Length, Numerical Approximations.

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257 Futures Trading: Design of a Strategy

Authors: Jan Zeman

Abstract:

The paper describes the futures trading and aims to design the speculators trading strategy. The problem is formulated as the decision making task and such as is solved. The solution of the task leads to complex mathematical problems and the approximations of the decision making is demanded. Two kind of approximation are used in the paper: Monte Carlo for the multi-step prediction and iteration spread in time for the optimization. The solution is applied to the real-market data and the results of the off-line experiments are presented.

Keywords: futures trading, decision making

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256 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

Authors: N. M. A. Nik Long, Z. K. Eshkuvatov, M. Yaghobifar, M. Hasan

Abstract:

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

Keywords: Approximation, Galerkin method, Integral equations, Laguerre polynomial.

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255 A Simplified Distribution for Nonlinear Seas

Authors: M. A. Tayfun, M. A. Alkhalidi

Abstract:

The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

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254 A Robust LS-SVM Regression

Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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253 Searching the Efficient Frontier for the Coherent Covering Location Problem

Authors: Felipe Azocar Simonet, Luis Acosta Espejo

Abstract:

In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: Coherent covering location problem, efficient frontier, Lagrangian relaxation, data envelopment analysis.

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252 Dominant Correlation Effects in Atomic Spectra

Authors: Hubert Klar

Abstract:

High double excitation of two-electron atoms has been investigated using hyperpherical coordinates within a modified adiabatic expansion technique. This modification creates a novel fictitious force leading to a spontaneous exchange symmetry breaking at high double excitation. The Pauli principle must therefore be regarded as approximation valid only at low excitation energy. Threshold electron scattering from high Rydberg states shows an unexpected time reversal symmetry breaking. At threshold for double escape we discover a broad (few eV) Cooper pair.

Keywords: Correlation, resonances, threshold ionization, Cooper pair.

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251 A Contractor for the Symmetric Solution Set

Authors: Milan Hladik

Abstract:

The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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250 Direct Method for Converting FIR Filter with Low Nonzero Tap into IIR Filter

Authors: Jeong Hye Moon, Byung Hoon Kang, PooGyeon Park

Abstract:

In this paper, we proposed the direct method for converting Finite-Impulse Response (FIR) filter with low nonzero tap into Infinite-Impulse Response (IIR) filter using the pre-determined table. The prony method is used by ghost cancellator which is IIR approximation to FIR filter which is better performance than IIR and have much larger calculation difference. The direct method for many ghost combination with low nonzero tap of NTSC(National Television System Committee) TV signal in Korea is described. The proposed method is illustrated with an example.

Keywords: NTSC, Ghost cancellation, FIR, IIR, Prony method.

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249 Optimal Control Problem, Quasi-Assignment Problem and Genetic Algorithm

Authors: Omid S. Fard, Akbar H. Borzabadi

Abstract:

In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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248 Approximation Approach to Linear Filtering Problem with Correlated Noise

Authors: Hong Son Hoang, Remy Baraille

Abstract:

The (sub)-optimal soolution of linear filtering problem with correlated noises is considered. The special recursive form of the class of filters and criteria for selecting the best estimator are the essential elements of the design method. The properties of the proposed filter are studied. In particular, for Markovian observation noise, the approximate filter becomes an optimal Gevers-Kailath filter subject to a special choice of the parameter in the class of given linear recursive filters.

Keywords: Linear dynamical system, filtering, minimum meansquare filter, correlated noise

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247 On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations

Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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246 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems

Authors: Jalil Rashidinia, Reza Jalilian

Abstract:

In this paper we use quintic non-polynomial spline functions to develop numerical methods for approximation to the solution of a system of fourth-order boundaryvalue problems associated with obstacle, unilateral and contact problems. The convergence analysis of the methods has been discussed and shown that the given approximations are better than collocation and finite difference methods. Numerical examples are presented to illustrate the applications of these methods, and to compare the computed results with other known methods.

Keywords: Quintic non-polynomial spline, Boundary formula, Convergence, Obstacle problems.

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245 Numerical Calculation of the Ionization Energy of Donors in a Cubic Quantum well and Wire

Authors: Sara Sedaghat, Mahmood Barati, Iraj Kazeminezhad

Abstract:

The ionization energy in semiconductor systems in nano scale was investigated by using effective mass approximation. By introducing the Hamiltonian of the system, the variational technique was employed to calculate the ground state and the ionization energy of a donor at the center and in the case that the impurities are randomly distributed inside a cubic quantum well. The numerical results for GaAs/GaAlAs show that the ionization energy strongly depends on the well width for both cases and it decreases as the well width increases. The ionization energy of a quantum wire was also calculated and compared with the results for the well.

Keywords: quantum well, quantum wire, quantum dot, impuritystate

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244 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems

Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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243 The Evaluation of the Performance of Different Filtering Approaches in Tracking Problem and the Effect of Noise Variance

Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

Abstract:

Performance of different filtering approaches depends on modeling of dynamical system and algorithm structure. For modeling and smoothing the data the evaluation of posterior distribution in different filtering approach should be chosen carefully. In this paper different filtering approaches like filter KALMAN, EKF, UKF, EKS and smoother RTS is simulated in some trajectory tracking of path and accuracy and limitation of these approaches are explained. Then probability of model with different filters is compered and finally the effect of the noise variance to estimation is described with simulations results.

Keywords: Gaussian approximation, KALMAN smoother, Parameter estimation.

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242 A Numerical Model for Studying Convectional Lifting Processes in the Tropics

Authors: Chantawan Noisri, Robert Harold Buchanan Exell

Abstract:

A simple model for studying convectional lifting processes in the tropics is described in this paper with some tests of the model in dry air. The model consists of the density equation, the wind equation, the vertical velocity equation, and the temperature equation. The model domain is two-dimensional with length 100 km and height 17.5 km. Plan for experiments to investigate the effects of the heating surface, the deep convection approximation and the treatment of velocities at the boundaries are discussed. Equations for the simplified treatment of moisture in the atmosphere in future numerical experiments are also given.

Keywords: Numerical weather prediction, Finite differences, Convection lifting.

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241 A Comparison of Exact and Heuristic Approaches to Capital Budgeting

Authors: Jindřiška Šedová, Miloš Šeda

Abstract:

This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. We show the problem representation and parameter settings for a genetic algorithm framework.

Keywords: Capital budgeting, knapsack problem, GAMS, heuristic method, genetic algorithm.

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240 Further Investigation of Elastic Scattering of 16O on 12C at Different Energies

Authors: Sh. Hamada, N. Burtebayev, N. Amangeldi, A. Amar

Abstract:

The aim of this work is to study the elastic transfer phenomenon which takes place in the elastic scattering of 16O on 12C at energies near the Coulomb barrier. Where, the angular distribution decrease steadily with increasing the scattering angle, then the cross section will increase at backward angles due to the α-transfer process. This reaction was also studied at different energies for tracking the nuclear rainbow phenomenon. The experimental data of the angular distribution at these energies were compared to the calculation predictions. The optical potential codes such as SPIVAL and Distorted Wave Born Approximation (DWUCK5) were used in analysis.

Keywords: Transfer reaction, DWBA, Elastic Scattering, Optical Potential Codes.

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239 Prediction of Computer and Video Game Playing Population: An Age Structured Model

Authors: T. K. Sriram, Joydip Dhar

Abstract:

Models based on stage structure have found varied applications in population models. This paper proposes a stage structured model to study the trends in the computer and video game playing population of US. The game paying population is divided into three compartments based on their age group. After simulating the mathematical model, a forecast of the number of game players in each stage as well as an approximation of the average age of game players in future has been made.

Keywords: Age structure, Forecasting, Mathematical modeling, Stage structure.

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238 Variational Evolutionary Splines for Solving a Model of Temporomandibular Disorders

Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

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237 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations

Authors: M. A. Koroma, C. Zhan, A. F. Kamara, A. B. Sesay

Abstract:

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

Keywords: Laplace decomposition, pantograph equations, exact solution, numerical solution, approximate solution.

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236 An Efficient Iterative Updating Method for Damped Structural Systems

Authors: Jiashang Jiang

Abstract:

Model updating is an inverse eigenvalue problem which concerns the modification of an existing but inaccurate model with measured modal data. In this paper, an efficient gradient based iterative method for updating the mass, damping and stiffness matrices simultaneously using a few of complex measured modal data is developed. Convergence analysis indicates that the iterative solutions always converge to the unique minimum Frobenius norm symmetric solution of the model updating problem by choosing a special kind of initial matrices.

Keywords: Model updating, iterative algorithm, damped structural system, optimal approximation.

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235 Mathematical Reconstruction of an Object Image Using X-Ray Interferometric Fourier Holography Method

Authors: M. K. Balyan

Abstract:

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: Dynamical diffraction, hologram, object image, X-ray holography.

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234 Thermoelastic Damping of Inextensional Hemispherical Shell

Authors: S. Y. Choi, Y. H. Na, J. H. Kim

Abstract:

In this work, thermoelastic damping effect on the hemi- spherical shells is investigated. The material is selected silicon, and heat conduction equation for thermal flow is solved to obtain the temperature profile in which bending approximation with inextensional assumption of the model. Using the temperature profile, eigen-value analysis is performed to get the natural frequencies of hemispherical shells. Effects of mode numbers, radii and radial thicknesses of the model on the natural frequencies are analyzed in detail. Furthermore, the quality factor (Q-factor) is defined, and discussed for the ring and hemispherical shell.

Keywords: Thermoelastic damping, hemispherical shell, quality factor

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233 A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations

Authors: Jinfeng Wang, Yang Liu, Hong Li

Abstract:

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations

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