Search results for: dropping method

Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

Abstract:

The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

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Authors: Maysam Shahsavari, Seyed Jamalaldin Haddadi

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There are several methods to localize a mobile robot such as relative, absolute and probabilistic. In this paper, particle filter due to its simple implementation and the fact that it does not need to know to the starting position will be used. This method estimates the position of the mobile robot using a probabilistic distribution, relying on a known map of the environment instead of predicting it. Afterwards, it updates this estimation by reading input sensors and control commands. To receive information from the surrounding world, distance to obstacles, for example, a Kinect is used which is much cheaper than a laser range finder. Finally, after explaining the Adaptive Particle Filter method and its implementation in detail, we will compare this method with the dead reckoning method and show that this method is much more suitable for situations in which we have a map of the environment.

Keywords: particle filter, localization, methods, odometry, kinect

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Authors: Mohammad Mojtahedpoor

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In this paper, it has been studied the method of optimal design of the supersonic nozzle. It could make viscous axisymmetric nozzles that the quality of their outlet flow is quite desired. In this method, it is optimized the divergent nozzle, at first. The initial divergent nozzle contour is designed through the method of characteristics and adding a suitable boundary layer to the inviscid contour. After that, it is made a proper grid and then simulated flow by the numerical solution and AUSM+ method by using the operation boundary condition. At the end, solution outputs are investigated and optimized. The numerical method has been validated with experimental results. Also, in order to evaluate the effectiveness of the present method, the nozzles compared with the previous studies. The comparisons show that the nozzles obtained through this method are sufficiently better in some conditions, such as the flow uniformity, size of the boundary layer, and obtained an axial length of the nozzle. Designing the convergent nozzle part affects by flow uniformity through changing its axial length and input diameter. The results show that increasing the length of the convergent part improves the output flow uniformity.

Keywords: nozzle, supersonic, optimization, characteristic method, CFD

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Assiya Madenovna Borsynbayeva, Kairat Altynbekovich Turgenbayev, Nikolay Petrovich Ivanov

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In this article presents the results of rapid diagnostics of tuberculosis in comparison with classical bacteriological method. The proposed method of rapid diagnosis of tuberculosis than bacteriological method allows shortening the time of diagnosis to 7 days, to visualize the growth of mycobacteria in the semi-liquid medium and differentiate the type of mycobacterium. Fast definition of Mycobacterium tuberculosis and its derivatives in the culture medium is a new and promising direction in the diagnosis of tuberculosis.

Keywords: animal diagnosis of tuberculosis, bacteriological diagnostics, antigen, specific antibodies, immunological reaction

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Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: F. J. Adeyeye, D. Eni, K. M. Okedoye

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In this paper we present a Hybrid of Adomian decomposition method (ADM). This is the substitution of a One-step method of Taylor’s series approximation of orders I and II, into the nonlinear part of Adomian decomposition method resulting in a convergent series scheme. This scheme is applied to solve some Logistic problems represented as Abelian differential equation and the results are compared with the actual solution and Runge-kutta of order IV in order to ascertain the accuracy and efficiency of the scheme. The findings shows that the scheme is efficient enough to solve logistic problems considered in this paper.

Keywords: Adomian decomposition method, nonlinear part, one-step method, Taylor series approximation, hybrid of Adomian polynomial, logistic problem, Malthusian parameter, Verhulst Model

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Authors: Abid Fida Masih

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Forced degradation study of Rifaximin was conducted to determine the stability indicating potential of HPLC testing method for detection of Rifaximin in formulated tablets to be employed for quality control and stability testing. The questioned method applied with mobile phase methanol: water (70:30), 5µm, 250 x 4.6mm, C18 column, wavelength 293nm and flow rate of 1.0 ml/min. Forced degradation study was performed under oxidative, acidic, basic, thermal and photolytic conditions. The applied method successfully determined the degradation products after acidic and basic degradation without interfering with Rifaximin detection. Therefore, the method was said to be stability indicating and can be applied for quality control and stability testing of Rifaxmin tablets during its shelf life.

Keywords: forced degradation, high-performance liquid chromatography, method validation, rifaximin, stability indicating method

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: S. Zenhari, M. R. Hematiyan, A. Khosravifard, M. R. Feizi

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The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains.

Keywords: boundary element method, method of fundamental solutions, elasticity, potential problem, convex domain, concave domain

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Authors: Junyou Shi, Weiwei Cui

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Testability modeling is a commonly used method in testability design and analysis of system. A dependency matrix will be obtained from testability modeling, and we will give a quantitative evaluation about fault detection and isolation. Based on the dependency matrix, we can obtain the diagnosis tree. The tree provides the procedures of the fault detection and isolation. But the dependency matrix usually includes built-in test (BIT) and manual test in fact. BIT runs the test automatically and is not limited by the procedures. The method above cannot give a more efficient diagnosis and use the advantages of the BIT. A Comprehensive method of fault detection and isolation is proposed. This method combines the advantages of the BIT and Manual test by splitting the matrix. The result of the case study shows that the method is effective.

Keywords: fault detection, fault isolation, testability modeling, BIT

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

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Authors: Kazuya Sato, Toru Kasahara, Junji Kuroda

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In this paper, an autonomous hovering control method of multicopter using only Web camera is proposed. Recently, various control method of an autonomous flight for multicopter are proposed. But, in the previously proposed methods, a motion capture system (i.e., OptiTrack) and laser range finder are often used to measure the position and posture of multicopter. To achieve an autonomous flight control of multicopter with simple equipment, we propose an autonomous flight control method using AR marker and Web camera. AR marker can measure the position of multicopter with Cartesian coordinate in three dimensional, then its position connects with aileron, elevator, and accelerator throttle operation. A simple PID control method is applied to the each operation and adjust the controller gains. Experimental result are given to show the effectiveness of our proposed method. Moreover, another simple operation method for autonomous flight control multicopter is also proposed.

Keywords: autonomous hovering control, multicopter, Web camera, operation

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Authors: Hsiang-Wen Tang, Cheng-Ying Lo

Abstract:

In this study, the static behavior of super elliptical Winkler plate is analyzed by applying the double side approach method. The lack of information about super elliptical Winkler plates is the motivation of this study and we use the double side approach method to solve this problem because of its superior ability on efficiently treating problems with complex boundary shape. The double side approach method has the advantages of high accuracy, easy calculation procedure and less calculation load required. Most important of all, it can give the error bound of the approximate solution. The numerical results not only show that the double side approach method works well on this problem but also provide us the knowledge of static behavior of super elliptical Winkler plate in practical use.

Keywords: super elliptical winkler plate, double side approach method, error bound, mechanic

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Authors: Beciri Mohamed Walid

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Some architectural conditions required some shapes often lead to an irregular distribution of masses, rigidities and resistances. The main object of the present study consists in estimating the influence of the irregularity both in plan and in elevation which presenting some structures on the dynamic characteristics and his influence on the behavior of this structures. To do this, it is necessary to make apply both dynamic methods proposed by the RPA99 (spectral modal method and method of analysis by accelerogram) on certain similar prototypes and to analyze the parameters measuring the answer of these structures and to proceed to a comparison of the results.

Keywords: structure, irregular, code, seismic, method, force, period

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Authors: Shashikant R. Kuchekar, Shivaji D. Pulate, Vishwas B. Gaikwad

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A simple and selective method is developed for solvent extraction spectrophotometric determination of antimony(III) using O-Methylphenyl Thiourea (OMPT) as a sensitive chromogenic chelating agent. The basis of proposed method is formation of antimony(III)-OMPT complex was extracted with 0.0025 M OMPT in chloroform from aqueous solution of antimony(III) in 1.0 M perchloric acid. The absorbance of this complex was measured at 297 nm against reagent blank. Beer’s law was obeyed up to 15µg mL-1 of antimony(III). The Molar absorptivity and Sandell’s sensitivity of the antimony(III)-OMPT complex in chloroform are 16.6730 × 103 L mol-1 cm-1 and 0.00730282 µg cm-2 respectively. The stoichiometry of antimony(III)-OMPT complex was established from slope ratio method, mole ratio method and Job’s continuous variation method was 1:2. The complex was stable for more than 48 h. The interfering effect of various foreign ions was studied and suitable masking agents are used wherever necessary to enhance selectivity of the method. The proposed method is successfully applied for determination of antimony(III) from real samples alloy and synthetic mixtures. Repetition of the method was checked by finding relative standard deviation (RSD) for 10 determinations which was 0.42%.

Keywords: solvent extraction, antimony, spectrophotometry, real sample analysis

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Authors: Liping Yang, Curran Crawford, Jr. Ren, Zhengyi Ren

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Considering the cost evaluation and the stress analysis, a fuzzy satisfactory optimization (FSO) method has been developed for a hybrid composite flywheel. To evaluate the cost, the cost coefficients of the flywheel components are obtained through calculating the weighted sum of the scores of the material manufacturability, the structure character, and the material price. To express the satisfactory degree of the energy, the cost, and the mass, the satisfactory functions are proposed by using the decline function and introducing a satisfactory coefficient. To imply the different significance of the objectives, the object weight coefficients are defined. Based on the stress analysis of composite material, the circumferential and radial stresses are considered into the optimization formulation. The simulations of the FSO method with different weight coefficients and storage energy density optimization (SEDO) method of a flywheel are contrasted. The analysis results show that the FSO method can satisfy different requirements of the designer and the FSO method with suitable weight coefficients can replace the SEDO method.

Keywords: flywheel energy storage, fuzzy, optimization, stress analysis

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Hakiki Kheira, Belhamiti Omar

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In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

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Authors: Ophir Nave

Abstract:

In our research, we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems (SPS). The SPVF method enables us to understand the complex system, and simplify the calculations. Later powerful analytical, numerical and asymptotic methods (e.g method of integral (invariant) manifold (MIM), the homotopy analysis method (HAM) etc.) can be applied to each subsystem. We compare the results obtained by the methods of integral invariant manifold and SPVF apply to spray droplets combustion model. The research deals with the development of an innovative method for extracting fast and slow variables in physical mathematical models. The method that we developed called singular perturbed vector field. This method based on a numerical algorithm applied to global quasi linearization applied to given physical model. The SPVF method applied successfully to combustion processes. Our results were compared to experimentally results. The SPVF is a general numerical and asymptotical method that reveals the hierarchy (multi-scale system) of a given system.

Keywords: polydisperse spray, model reduction, asymptotic analysis, multi-scale systems

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Authors: Mesut BALIBEY, Serpil TÜRKYILMAZ

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A popular topic in the econometrics and time series area is the cointegrating relationships among the components of a nonstationary time series. Engle and Granger’s least squares method and Johansen’s conditional maximum likelihood method are the most widely-used methods to determine the relationships among variables. Furthermore, a method proposed to test a unit root based on the periodogram ordinates has certain advantages over conventional tests. Periodograms can be calculated without any model specification and the exact distribution under the assumption of a unit root is obtained. For higher order processes the distribution remains the same asymptotically. In this study, in order to indicate advantages over conventional test of periodograms, we are going to examine a possible relationship between tourism and economic growth during the period 1999:01-2010:12 for Turkey by using periodogram method, Johansen’s conditional maximum likelihood method, Engle and Granger’s ordinary least square method.

Keywords: cointegration, economic growth, periodogram ordinate, tourism

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Authors: Shigeyuki Haruyama, Ken Kaminishi, Junji Kaneko, Tadayuki Kyoutani, Siti Ruhana Omar, Oke Oktavianty

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This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physics fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

Keywords: system model, physical models, empirical models, conservation law, differential algebraic equation, object-oriented

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Authors: Abouzar Kaboudian, Boo Cheong Khoo

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The Ghost Solid Method (GSM) based algorithms have been extensively used for numerical calculation of wave propagation in the limit of abrupt changes in materials. In this work, we present a unified version of the GSMs that can be successfully applied to both abrupt as well as smooth changes of the material properties in a medium. The application of this method enables us to use the previously-matured numerical algorithms which were developed to be applied to homogeneous mediums, with only minor modifications. This method is developed for one-dimensional settings and its extension to multi-dimensions is briefly discussed. Various numerical experiments are presented to show the applicability of this unified GSM to wave propagation problems in sharply as well as smoothly varying mediums.

Keywords: elastic solid, functionally graded material, ghost solid method, solid-solid interaction

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: D. Remache, M. Semaan, C. Baron, M. Pithioux, P. Chabrand, J. M. Rossi, J. L. Milan

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A good understanding of the mechanical properties of the bone implies a better understanding of its various diseases, such as osteoporosis. Berkovich nanoindentation tests were performed on the human cortical bone to extract its orthotropic parameters. The nanoindentation experiments were then simulated by the finite element method. Different configurations of interactions between the tip indenter and the bone were simulated. The orthotropic parameters of the material were identified by the inverse method for each configuration. The friction effect on the bone mechanical properties was then discussed. It was found that the inverse method using the finite element method is a very efficient method to predict the mechanical behavior of the bone.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approaches

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Authors: Kunya Bowornchockchai

Abstract:

The objective of this research is to forecast the monthly exchange rate between Thai baht and the US dollar and to compare two forecasting methods. The methods are Box-Jenkins’ method and Holt’s method. Results show that the Box-Jenkins’ method is the most suitable method for the monthly Exchange Rate between Thai Baht and the US Dollar. The suitable forecasting model is ARIMA (1,1,0)  without constant and the forecasting equation is Y_t = Y_t-1 + 0.3691 (Y_t-1 - Y_t-2) When Y_t  is the time series data at time t, respectively.

Keywords: Box–Jenkins method, Holt’s method, mean absolute percentage error (MAPE), exchange rate

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Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cycling parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon

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