Search results for: systems of linear equations.

Authors: Michal Polanský, C. Ardil

Abstract:

This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.

Keywords: H norm, Linear Matrix Inequalities, Observers, Takagi-Sugeno Systems, Parallel Distributed Compensation

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Authors: Sachin Bhalekar, Varsha Daftardar-Gejji

Abstract:

In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.

Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

Abstract:

The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.

The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.

Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,

Keywords: Non-linear vibrations, Annular plates, Large vibration amplitudes.

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Authors: Zarina Bibi, I., Khairil Iskandar, O.

Abstract:

In this paper, parallelism in the solution of Ordinary Differential Equations (ODEs) to increase the computational speed is studied. The focus is the development of parallel algorithm of the two point Block Backward Differentiation Formulas (PBBDF) that can take advantage of the parallel architecture in computer technology. Parallelism is obtained by using Message Passing Interface (MPI). Numerical results are given to validate the efficiency of the PBBDF implementation as compared to the sequential implementation.

Keywords: Ordinary differential equations, parallel.

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Authors: Masoud Sadeghian, Alireza Fatehi

Abstract:

One of the most important parts of a cement factory is the cement rotary kiln which plays a key role in quality and quantity of produced cement. In this part, the physical exertion and bilateral movement of air and materials, together with chemical reactions take place. Thus, this system has immensely complex and nonlinear dynamic equations. These equations have not worked out yet. Only in exceptional case; however, a large number of the involved parameter were crossed out and an approximation model was presented instead. This issue caused many problems for designing a cement rotary kiln controller. In this paper, we presented nonlinear predictor and simulator models for a real cement rotary kiln by using nonlinear identification technique on the Locally Linear Neuro- Fuzzy (LLNF) model. For the first time, a simulator model as well as a predictor one with a precise fifteen minute prediction horizon for a cement rotary kiln is presented. These models are trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. At the end, the characteristics of these models are expressed. Furthermore, we presented the pros and cons of these models. The data collected from White Saveh Cement Company is used for modeling.

Keywords: Cement rotary kiln, nonlinear identification, Locally Linear Neuro-Fuzzy model.

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Authors: J. Sulaiman, M. Othman, M. K. Hasan

Abstract:

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

Keywords: MEG iteration, second-order finite difference, weighted parameter.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: H∞ control, Takagi-Sugeno (TS) fuzzy model, Linear Matrix Inequalities (LMIs), Descriptor systems.

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Authors: Chih-Ling Huang, Wen-Yi Lin, Kuo-Mo Hsiao

Abstract:

A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.

Keywords: Flapping vibration, Inclination angle, Natural frequency, Rotating beam.

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Authors: R. Bhargava, Sonam Singh

Abstract:

In the present study, a numerical analysis is carried out to investigate unsteady MHD (magneto-hydrodynamic) flow and heat transfer of a non-Newtonian second grade viscoelastic fluid over an oscillatory stretching sheet. The flow is induced due to an infinite elastic sheet which is stretched oscillatory (back and forth) in its own plane. Effect of viscous dissipation and joule heating are taken into account. The non-linear differential equations governing the problem are transformed into system of non-dimensional differential equations using similarity transformations. A newly developed meshfree numerical technique Element free Galerkin method (EFGM) is employed to solve the coupled non linear differential equations. The results illustrating the effect of various parameters like viscoelastic parameter, Hartman number, relative frequency amplitude of the oscillatory sheet to the stretching rate and Eckert number on velocity and temperature field are reported in terms of graphs and tables. The present model finds its application in polymer extrusion, drawing of plastic films and wires, glass, fiber and paper production etc.

Keywords: EFGM, MHD, Oscillatory stretching sheet, Unsteady, Viscoelastic

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Authors: Kazuyoshi Mori, Keisuke Hashimoto

Abstract:

In this paper, we consider the two-stage compensator designs of SISO plants. As an investigation of the characteristics of the two-stage compensator designs, which is not well investigated yet, of SISO plants, we implement three dimensional visualization systems of output signals and optimization system for SISO plants by the parametrization of stabilizing controllers based on the two-stage compensator design. The system runs on Mathematica by using “Three Dimensional Surface Plots,” so that the visualization can be interactively manipulated by users. In this paper, we use the discrete-time LTI system model. Even so, our approach is the factorization approach, so that the result can be applied to many linear models.

Keywords: Linear systems, visualization, optimization, two-Stage compensator design, Mathematica.

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Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability of wake-shear layers in two-phase shallow flows is analyzed in the present paper. Stability analysis is based on two-dimensional shallow water equations. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. Linear stability curves are obtained for different values of the particle loading parameter, the velocity ratio and the velocity deficit. It is shown that the increase in the velocity ratio destabilizes the flow. The particle loading parameter has a stabilizing effect on the flow. The role of the velocity deficit is also destabilizing: the increase of the velocity deficit leads to less stable flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

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Authors: Michela Lecca, Stefano Messelodi

Abstract:

A new automatic system for the recognition and re¬construction of resealed and/or rotated partially occluded objects is presented. The objects to be recognized are described by 2D views and each view is occluded by several half-planes. The whole object views and their visible parts (linear cuts) are then stored in a database. To establish if a region R of an input image represents an object possibly occluded, the system generates a set of linear cuts of R and compare them with the elements in the database. Each linear cut of R is associated to the most similar database linear cut. R is recognized as an instance of the object 0 if the majority of the linear cuts of R are associated to a linear cut of views of 0. In the case of recognition, the system reconstructs the occluded part of R and determines the scale factor and the orientation in the image plane of the recognized object view. The system has been tested on two different datasets of objects, showing good performance both in terms of recognition and reconstruction accuracy.

Keywords: Occluded Object Recognition, Shape Reconstruction, Automatic Self-Adaptive Systems, Linear Cut.

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Authors: Rampal Singh, S. Balasundaram

Abstract:

In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: Gholamreza Hojjati, Kourosh Parand

Abstract:

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

Keywords: Lane-Emden type equations, nonlinear ODE, stiff problems, multistep methods, astrophysics.

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

Abstract:

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: Nonlinear optics, propagation equation, plasmonic waveguide.

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Authors: Rafael Jorge Menezes Santos, Ginalber Luiz de Oliveira Serra, Carlos César Teixeira Ferreira

Abstract:

This paper proposes a methodology for analysis of the dynamic behavior of a robotic manipulator in continuous time. Initially this system (nonlinear system) will be decomposed into linear submodels and analyzed in the context of the Linear and Parameter Varying (LPV) Systems. The obtained linear submodels, which represent the local dynamic behavior of the robotic manipulator in some operating points were grouped in a Takagi-Sugeno fuzzy structure. The obtained fuzzy model was analyzed and validated through analog simulation, as universal approximator of the robotic manipulator.

Keywords: modeling of nonlinear dynamic systems, Takagi- Sugeno fuzzy model, Linear and Parameter Varying (LPV) System.

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: Amir Badkoubeh, Guchuan Zhu

Abstract:

This paper addresses the problem of asymptotic tracking control of a linear parabolic partial differential equation with indomain point actuation. As the considered model is a non-standard partial differential equation, we firstly developed a map that allows transforming this problem into a standard boundary control problem to which existing infinite-dimensional system control methods can be applied. Then, a combination of energy multiplier and differential flatness methods is used to design an asymptotic tracking controller. This control scheme consists of stabilizing state-feedback derived from the energy multiplier method and feed-forward control based on the flatness property of the system. This approach represents a systematic procedure to design tracking control laws for a class of partial differential equations with in-domain point actuation. The applicability and system performance are assessed by simulation studies.

Keywords: Tracking Control, In-domain point actuation, PartialDifferential Equations.

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Authors: Vineet K. Srivastava, Mukesh K. Awasthi, Mohammad Tamsir

Abstract:

A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.

Keywords: Burgers’ equation, Implicit Finite-difference method, Newton’s method, Gauss elimination with partial pivoting.

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Authors: Randhir Singh Baghel, Govind Shay Sharma

Abstract:

In this paper, we explore an ecosystem that contains a three-species food chain. The first and second species are in competition with one another for resources. However, the third species plays an important role in providing non-linear Crowley-Martin functional support for the first species. Additionally, the third species consumes the second species in a linear fashion, taking advantage of the available resources. This intricate balance ensures the survival of all three species in the ecosystem. A set of non-linear isolated first-order differential equations establish this model. We examine the system's stability at all potential equilibrium locations using the perturbed technique. Furthermore, by spending a lot of time observing the species in their natural habitat, the numerical illustrations at suitable parameter values for the model are shown.

Keywords: Competition, predator, response function, local stability, numerical simulations.

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Authors: Ahmet Tekcan

Abstract:

Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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Authors: Peiangpob Monnuanprang

Abstract:

In this paper we study the transformation of Euler equations  1 , u u u Pf t (ρ ∂) + ⋅∇ = − ∇ + ∂ G G G G ∇⋅ = u 0, G where (ux, t) G G is the velocity of a fluid, P(x, t) G is the pressure of a fluid andρ (x, t) G is density. First of all, we rewrite the Euler equations in terms of new unknown functions. Then, we introduce new independent variables and transform it to a new curvilinear coordinate system. We obtain the Euler equations in the new dependent and independent variables. The governing equations into two subsystems, one is hyperbolic and another is elliptic.

Keywords: Euler equations, transformation, hyperbolic, elliptic

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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Authors: Wookyong Kwon, Sangmoon Lee

Abstract:

In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: Sherif. S. Nafee, Ameer. K. Al-Ramady, Salem. A. Shaheen

Abstract:

The analytical prediction of the decay heat results from the fast neutron fission of actinides was initiated under a project, 10-MAT1134-3, funded by king Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, managed by a team from King Abdulaziz University (KAU), Saudi Arabia, and supervised by Argonne National Laboratory (ANL) has collaborated with KAU's team to assist in the computational analysis. In this paper, the numerical solution of coupled linear differential equations that describe the decays and buildups of minor fission product MFA, has been used to predict the total decay heat and its components from the fast neutron fission of 235U and 239Pu. The reliability of the present approach is illustrated via systematic comparisons with the measurements reported by the University of Tokyo, in YAYOI reactor.

Keywords: Decay heat, fast neutron fission, and Numerical Solution of Linear Differential Equations.

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Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam

Abstract:

Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.

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Authors: D. Vijayakumar, R. K. Nema

Abstract:

Over Current Relays (OCRs) and Directional Over Current Relays (DOCRs) are widely used for the radial protection and ring sub transmission protection systems and for distribution systems. All previous work formulates the DOCR coordination problem either as a Non-Linear Programming (NLP) for TDS and Ip or as a Linear Programming (LP) for TDS using recently a social behavior (Particle Swarm Optimization techniques) introduced to the work. In this paper, a Modified Particle Swarm Optimization (MPSO) technique is discussed for the optimal settings of DOCRs in power systems as a Non-Linear Programming problem for finding Ip values of the relays and for finding the TDS setting as a linear programming problem. The calculation of the Time Dial Setting (TDS) and the pickup current (Ip) setting of the relays is the core of the coordination study. PSO technique is considered as realistic and powerful solution schemes to obtain the global or quasi global optimum in optimization problem.

Keywords: Directional over current relays, Optimization techniques, Particle swarm optimization, Power system protection.

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