Search results for: fundamental equations
3402 The Application of Variable Coefficient Jacobian elliptic Function Method to Differential-Difference Equations
Authors: Chao-Qing Dai
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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation
Procedia PDF Downloads 6643401 Electromagnetic Wave Propagation Equations in 2D by Finite Difference Method
Authors: N. Fusun Oyman Serteller
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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples. Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations
Procedia PDF Downloads 1393400 On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid
Authors: A. Giniatoulline
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A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid
Procedia PDF Downloads 2993399 Numerical Solutions of Fredholm Integral Equations by B-Spline Wavelet Method
Authors: Ritu Rani
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In this paper, we apply minimalistically upheld linear semi-orthogonal B-spline wavelets, exceptionally developed for the limited interim to rough the obscure function present in the integral equations. Semi-orthogonal wavelets utilizing B-spline uniquely developed for the limited interim and these wavelets can be spoken to in a shut frame. This gives a minimized help. Semi-orthogonal wavelets frame the premise in the space L²(R). Utilizing this premise, an arbitrary function in L²(R) can be communicated as the wavelet arrangement. For the limited interim, the wavelet arrangement cannot be totally introduced by utilizing this premise. This is on the grounds that backings of some premise are truncated at the left or right end purposes of the interim. Subsequently, an uncommon premise must be brought into the wavelet development on the limited interim. These functions are alluded to as the limit scaling functions and limit wavelet functions. B-spline wavelet method has been connected to fathom linear and nonlinear integral equations and their systems. The above method diminishes the integral equations to systems of algebraic equations and afterward these systems can be illuminated by any standard numerical methods. Here, we have connected Newton's method with suitable starting speculation for solving these systems.Keywords: semi-orthogonal, wavelet arrangement, integral equations, wavelet development
Procedia PDF Downloads 1733398 Reducing Total Harmonic Content of 9-Level Inverter by Use of Cuckoo Algorithm
Authors: Mahmoud Enayati, Sirous Mohammadi
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In this paper, a novel procedure to find the firing angles of the multilevel inverters of supply voltage and, consequently, to decline the total harmonic distortion (THD), has been presented. In order to eliminate more harmonics in the multilevel inverters, its number of levels can be lessened or pulse width modulation waveform, in which more than one switching occur in each level, be used. Both cases complicate the non-algebraic equations and their solution cannot be performed by the conventional methods for the numerical solution of nonlinear equations such as Newton-Raphson method. In this paper, Cuckoo algorithm is used to compute the optimal firing angle of the pulse width modulation voltage waveform in the multilevel inverter. These angles should be calculated in such a way that the voltage amplitude of the fundamental frequency be generated while the total harmonic distortion of the output voltage be small. The simulation and theoretical results for the 9-levels inverter offer the high applicability of the proposed algorithm to identify the suitable firing angles for declining the low order harmonics and generate a waveform whose total harmonic distortion is very small and it is almost a sinusoidal waveform.Keywords: evolutionary algorithms, multilevel inverters, total harmonic content, Cuckoo Algorithm
Procedia PDF Downloads 5293397 Analyses of the Constitutional Identity in Hungary: A Case Study on the Concept of Constitutionalism and Legal Continuity in New Fundamental Law of Hungary
Authors: Zsuzsanna Fejes
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The aim of this paper is to provide an overview of the legal history of constitutionalism in Hungary, in focus of the democratic transitions in 1989-1990, describing the historical and political background of the changes and presenting the main and most important features of the new democracy, and institutional and legal orders. In Hungary the evolved political, economic and moral crisis prior to the constitutional years 2010-11 had been such a constitutional moment, which led to an opportune and unavoidable change at the same time. The Hungarian constitutional power intended to adopt a new constitution, which was competent to create a common constitutional identity and to express a national unity. The Hungarian Parliament on 18th April 2011 passed the New Fundamental Law. The new Fundamental Law rich in national values meant a new challenge for the academics, lawyers, and political scientists. Not only the classical political science, but also the constitutional law and theory have to struggle with the interpretation of the new declarations about national constitutional values in the Fundamental Law. The main features and structure of the new Fundamental Law will be analysed, and given a detailed interpretation of the Preamble as a declaration of constitutional values. During the examination of the Preamble shall be cleared up the components of Hungarian statehood and national unity, individual and common human rights, the practical and theoretical demand on national sovereignty, and the content and possibilities for the interpretation of the achievements of the historical Constitution. These scopes of problems will be presented during the examination of the text of National Avowal, as a preamble of the Fundamental Law. It is examined whether the Fundamental Law itself could be suitable and sufficient means to citizens of Hungary to express the ideas therein as their own, it will be analysed how could the national and European common traditions, values and principles stated in the Fundamental Law mean maintenance in Hungary’s participation in the European integration.Keywords: common constitutional values, constitutionalism, national identity, national sovereignty, national unity, statehood
Procedia PDF Downloads 2903396 A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions
Authors: Xijun Yu, Zhenzhen Li, Zupeng Jia
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This paper presents a new cell-centered Lagrangian scheme for two-dimensional compressible flow. The new scheme uses a semi-Lagrangian form of the Euler equations. The system of equations is discretized by Discontinuous Galerkin (DG) method using the Taylor basis in Eulerian space. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently by a nodal solver. The mesh moves with the fluid flow. The time marching is implemented by a class of the Runge-Kutta (RK) methods. A WENO reconstruction is used as a limiter for the RKDG method. The scheme is conservative for the mass, momentum and total energy. The scheme maintains second-order accuracy and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.Keywords: cell-centered Lagrangian scheme, compressible Euler equations, RKDG method
Procedia PDF Downloads 5423395 Ambient Vibration Testing of Existing Buildings in Madinah
Authors: Tarek M. Alguhane, Ayman H. Khalil, M. N. Fayed, Ayman M. Ismail
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The elastic period has a primary role in the seismic assessment of buildings. Reliable calculations and/or estimates of the fundamental frequency of a building and its site are essential during analysis and design process. Various code formulas based on empirical data are generally used to estimate the fundamental frequency of a structure. For existing structures, in addition to code formulas and available analytical tools such as modal analyses, various methods of testing including ambient and forced vibration testing procedures may be used to determine dynamic characteristics. In this study, the dynamic properties of the 32 buildings located in the Madinah of Saudi Arabia were identified using ambient motions recorded at several, spatially-distributed locations within each building. Ambient vibration measurements of buildings have been analyzed and the fundamental longitudinal and transverse periods for all tested buildings are presented. The fundamental mode of vibration has been compared in plots with codes formulae (Saudi Building Code, EC8, and UBC1997). The results indicate that measured periods of existing buildings are shorter than that given by most empirical code formulas. Recommendations are given based on the common design and construction practice in Madinah city.Keywords: ambient vibration, fundamental period, RC buildings, infill walls
Procedia PDF Downloads 2573394 Analytical Solutions of Time Space Fractional, Advection-Dispersion and Whitham-Broer-Kaup Equations
Authors: Muhammad Danish Khan, Imran Naeem, Mudassar Imran
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In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.Keywords: modified Riemann-Liouville fractional derivative, lie-symmetries, optimal system, invariant solutions
Procedia PDF Downloads 4253393 Multidimensional Integral and Discrete Opial–Type Inequalities
Authors: Maja Andrić, Josip Pečarić
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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality
Procedia PDF Downloads 4293392 Superconvergence of the Iterated Discrete Legendre Galerkin Method for Fredholm-Hammerstein Equations
Authors: Payel Das, Gnaneshwar Nelakanti
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In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results.Keywords: hammerstein integral equations, spectral method, discrete galerkin, numerical quadrature, superconvergence
Procedia PDF Downloads 4643391 Study and Solving High Complex Non-Linear Differential Equations Applied in the Engineering Field by Analytical New Approach AGM
Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili
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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle
Procedia PDF Downloads 4613390 A Study of Flow near the Leading Edge of a Flat Plate by New Idea in Analytical Methods
Authors: M. R. Akbari, S. Akbari, L. Abdollahpour
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The present paper is concerned with calculating the 2-dimensional velocity profile of a viscous flow for an incompressible fluid along the leading edge of a flat plate by using the continuity and motion equations with a simple and innovative approach. A Comparison between Numerical method and AGM has been made and the results have been revealed that AGM is very accurate and easy and can be applied for a wide variety of nonlinear problems. It is notable that most of the differential equations can be solved in this approach which in the other approaches they do not have this capability. Moreover, there are some valuable benefits in this method of solving differential equations, for instance: Without any dimensionless procedure, we can solve many differential equation(s), that is, differential equations are directly solvable by this method. In addition, it is not necessary to convert variables into new ones. According to the afore-mentioned expressions which will be proved in this literature, the process of solving nonlinear differential equation(s) will be very simple and convenient in contrast to the other approaches.Keywords: leading edge, new idea, flat plate, incompressible fluid
Procedia PDF Downloads 2793389 Dynamic Stability of a Wings for Drone Aircraft Subjected to Parametric Excitation
Authors: Iyd Eqqab Maree, Habil Jurgen Bast
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Vibration control of machines and structures incorporating viscoelastic materials in suitable arrangement is an important aspect of investigation. The use of viscoelastic layers constrained between elastic layers is known to be effective for damping of flexural vibrations of structures over a wide range of frequencies. The energy dissipated in these arrangements is due to shear deformation in the viscoelastic layers, which occurs due to flexural vibration of the structures. Multilayered cantilever sandwich beam like structures can be used in aircrafts and other applications such as robot arms for effective vibration control. These members may experience parametric instability when subjected to time dependant forces. The theory of dynamic stability of elastic systems deals with the study of vibrations induced by pulsating loads that are parametric with respect to certain forms of deformation. The purpose of the present work is to investigate the dynamic stability of a three layered symmetric sandwich beam (Drone Aircraft wings ) subjected to an end periodic axial force . Equations of motion are derived using finite element method (MATLAB software). It is observed that with increase in core thickness parameter fundamental buckling load increases. The fundamental resonant frequency and second mode frequency parameter also increase with increase in core thickness parameter. Fundamental loss factor and second mode loss factor also increase with increase in core thickness parameter. Increase in core thickness parameter enhances the stability of the beam. With increase in core loss factor also the stability of the beam enhances. There is a very good agreement of the experimental results with the theoretical findings.Keywords: steel cantilever beam, viscoelastic material core, loss factor, transition region, MATLAB R2011a
Procedia PDF Downloads 4663388 Solving SPDEs by Least Squares Method
Authors: Hassan Manouzi
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We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method
Procedia PDF Downloads 4133387 Dynamic Behavior of Brain Tissue under Transient Loading
Authors: Y. J. Zhou, G. Lu
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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury
Procedia PDF Downloads 2653386 Finite Element Method for Solving the Generalized RLW Equation
Authors: Abdel-Maksoud Abdel-Kader Soliman
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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations
Procedia PDF Downloads 4853385 Cubical Representation of Prime and Essential Prime Implicants of Boolean Functions
Authors: Saurabh Rawat, Anushree Sah
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K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations. Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws, and different traits of Karnaugh Maps. Largest possible k- cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.rKeywords: K-maps, don’t care conditions, Boolean equations, cubes
Procedia PDF Downloads 3813384 Causal Relationship between Corporate Governance and Financial Information Transparency: A Simultaneous Equations Approach
Authors: Maali Kachouri, Anis Jarboui
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We focus on the causal relationship between governance and information transparency as well as interrelation among the various governance mechanisms. This paper employs a simultaneous equations approach to show this relationship in the Tunisian context. Based on an 8-year dataset, our sample covers 28 listed companies over 2006-2013. Our findings suggest that internal and external governance mechanisms are interdependent. Moreover, in order to analyze the causal effect between information transparency and governance mechanisms, we found evidence that information transparency tends to increase good corporate governance practices.Keywords: simultaneous equations approach, transparency, causal relationship, corporate governance
Procedia PDF Downloads 3473383 Three Dimensional Vibration Analysis of Carbon Nanotubes Embedded in Elastic Medium
Authors: M. Shaban, A. Alibeigloo
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This paper studies free vibration behavior of single-walled carbon nanotubes (SWCNTs) embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, nonlocal theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radius-to-length ratio.Keywords: carbon nanotubes, embedded, nonlocal, free vibration
Procedia PDF Downloads 4423382 Heat Transfer and Entropy Generation in a Partial Porous Channel Using LTNE and Exothermicity/Endothermicity Features
Authors: Mohsen Torabi, Nader Karimi, Kaili Zhang
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This work aims to provide a comprehensive study on the heat transfer and entropy generation rates of a horizontal channel partially filled with a porous medium which experiences internal heat generation or consumption due to exothermic or endothermic chemical reaction. The focus has been given to the local thermal non-equilibrium (LTNE) model. The LTNE approach helps us to deliver more accurate data regarding temperature distribution within the system and accordingly to provide more accurate Nusselt number and entropy generation rates. Darcy-Brinkman model is used for the momentum equations, and constant heat flux is assumed for boundary conditions for both upper and lower surfaces. Analytical solutions have been provided for both velocity and temperature fields. By incorporating the investigated velocity and temperature formulas into the provided fundamental equations for the entropy generation, both local and total entropy generation rates are plotted for a number of cases. Bifurcation phenomena regarding temperature distribution and interface heat flux ratio are observed. It has been found that the exothermicity or endothermicity characteristic of the channel does have a considerable impact on the temperature fields and entropy generation rates.Keywords: entropy generation, exothermicity or endothermicity, forced convection, local thermal non-equilibrium, analytical modelling
Procedia PDF Downloads 4103381 Analytical Solving of Nonlinear Differential Equations in the Nonlinear Phenomena for Viscos Fluids
Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin
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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena
Procedia PDF Downloads 2783380 Bound State Problems and Functional Differential Geometry
Authors: S. Srednyak
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We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos
Procedia PDF Downloads 663379 Chemical Reaction Effects on Unsteady MHD Double-Diffusive Free Convective Flow over a Vertical Stretching Plate
Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo
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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.Keywords: chemical reaction, MHD, double-diffusive, stretching plate
Procedia PDF Downloads 4043378 An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon
Authors: Haniye Dehestani, Yadollah Ordokhani
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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration
Procedia PDF Downloads 1613377 Modelling Structural Breaks in Stock Price Time Series Using Stochastic Differential Equations
Authors: Daniil Karzanov
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This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations
Procedia PDF Downloads 2013376 Second Order Analysis of Frames Using Modified Newmark Method
Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi
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The main purpose of this paper is to present the Modified Newmark Method as a method of non-linear frame analysis by considering the effect of the axial load (second order analysis). The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. This part of the investigation is performed to generalize the established method for the assemblage structures such as frameworks. As explained, the governing differential equations are non-linear and cannot be formulated easily due to unknown axial load of the struts in the frame. By the assumption of constant axial load, the governing equations are changed to linear ones in most methods. Since the modeling and the solutions of the non-linear form of the governing equations are cumbersome, the linear form of the equations would be used in the established method. However, according to the ability of the method to reconsider the minor omitted parameters in modeling during the solution procedure, the axial load in the elements at each stage of the iteration can be computed and applied in the next stage. Therefore, the ability of the method to present an accurate approach to the solutions of non-linear equations will be demonstrated again in this paper.Keywords: nonlinear, stability, buckling, modified newmark method
Procedia PDF Downloads 4193375 Study υ_4 Fundamental Band of 12 CD4 Molecule
Authors: Kaarour Abdelkrim, Ouardi Okkacha, Meskine Mohamed
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In this study, the υ_4 fundamental band of 12CD4 molecule has been studied by infrared spectroscopy with high resolution. Using XTDS and SPEVIEW software and the tensor formalism developed by ICB (laboratoire interdisciplinaire de Bourgogne) to several lines have been assigned and fitted with a standard deviation acceptable. This analysis allowed us to calculate several parameters of the molecule 12 CD4.Keywords: XTDS, SPEVIEW, tetrahedral tensorial formalism, rovibrational band
Procedia PDF Downloads 3223374 From Linear to Nonlinear Deterrence: Deterrence for Rising Power
Authors: Farhad Ghasemi
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Along with transforming the international system into a complex and chaotic system, the fundamental question arises: how can deterrence be reconstructed conceptually and theoretically in this system model? The deterrence system is much more complex today than it was seven decades ago. This article suggests that the perception of deterrence as a linear system is a fundamental mistake because it does not consider the new dynamics of the international system, including network power dynamics. The author aims to improve this point by focusing on complexity and chaos theories, especially their nonlinearity and cascading failure principles. This article proposes that the perception of deterrence as a linear system is a fundamental mistake, as the new dynamics of the surrounding international system do not take into account. The author recognizes deterrence as a nonlinear system and introduces it as a concept in strategic studies.Keywords: complexity, international system, deterrence, linear deterrence, nonlinear deterrence
Procedia PDF Downloads 1343373 Symbolic Computation for the Multi-Soliton Solutions of a Class of Fifth-Order Evolution Equations
Authors: Rafat Alshorman, Fadi Awawdeh
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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method
Procedia PDF Downloads 313