Search results for: fractional evolution equations

Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Abdi Ammar, Ouazir Youcef, Laissaoui Abdelmalek

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In this work, an approach based on transmission lines theory is presented. It is exploited for the calculation of overvoltage created by direct impacts of lightning waves on a guard cable of an overhead high-voltage line. First, we show the theoretical developments leading to the propagation equation, its discretization by finite difference time domain method (FDTD), and the resulting linear algebraic equations, followed by the calculation of the linear parameters of the line. The second step consists of solving the transmission lines system of equations by the FDTD method. This enabled us to determine the spatio-temporal evolution of the induced overvoltage.

Keywords: lightning surge, transient overvoltage, eddy current, FDTD, electromagnetic compatibility, ground wire

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Authors: Emanuel Guariglia

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In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry.

Keywords: Chebyshev wavelets, Fourier transform, connection coefficients, Taylor series, local fractional derivative, Cantor set

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: K. Y. Tseng, C. Y. Wu

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This paper employs a heuristic algorithm to solve engineering problems including truss structure optimization and optimal chiller loading (OCL) problems. Two different type algorithms, real-valued differential evolution (DE) and modified binary differential evolution (MBDE), are successfully integrated and then can obtain better performance in solving engineering problems. In order to demonstrate the performance of the proposed algorithm, this study adopts each one testing case of truss structure optimization and OCL problems to compare the results of other heuristic optimization methods. The result indicates that the proposed algorithm can obtain similar or better solution in comparing with previous studies.

Keywords: differential evolution, Truss structure optimization, optimal chiller loading, modified binary differential evolution

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Authors: Yuhei Kunihiro, Sorin V. Sabau, Kazuhiro Shibuya

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We study the molecular evolution of insulin from the metric geometry point of view. In mathematics, and particularly in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from the geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: metric geometry, evolution, insulin, C. elegans

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Authors: Mandy W. M. Chan, Samantha Y. N. Shek, Chi K. Yeung, Taro Kono, Henry H. L. Chan

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Fractional radiofrequency devices have shown to improve skin texture such as smoothness, rhytides, brightness as well as atrophic acne scars by increasing dermal thickness, dermal collagen content and dermal fibrillin content. The objective of the study is to assess the efficacy and adverse effects of this device on Asian patients with skin textural changes. In this study, 20 Chinese patients (ranging from 21-60 years old) with irregularities of skin texture, rhytides and acne scars were recruited. Patients received six treatments at 2-4 week intervals. Treatment was initiated with maximum energy tolerated and was adjustable during treatment if patients felt excessive discomfort. A total of two passes were delivered at each session. Physician assessment and standardized photographs were taken at baseline, all treatment visits and at one, two, and six month after final treatment. As a result, 17 patients were recruited and completed the study according to the study protocol. One patient withdrew after the first treatment due to reaction to local anesthesia and two patients were lost to follow-up. At six months follow-up, 71% of the patients were satisfied and 24% were very satisfied, while treatment physician reported various degrees of improvement based on the global assessment scale in 60% of the subjects. Anticipated side effects including erythema, edema, pinpoint bleeding, scabs formation and flare of acne were recorded, but there were no serious adverse effects noted. Conclude up, the use of fractional radiofrequency improves skin texture and appears to be safe in Asian patients. No long-term serious adverse effect was noted.

Keywords: Asian, fractional radiogrequency, skin, texture

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Authors: Parisa Khoshvaght, Mehdi Hosseinzadeh

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During the past few years, the Residue Number System (RNS) has been receiving considerable interest due to its parallel and fault-tolerant properties. This system is a useful tool for Digital Signal Processing (DSP) since it can support parallel, carry-free, high-speed and low power arithmetic. One of the drawbacks of Residue Number System is the fractional numbers, that is, the corresponding circuit is very hard to realize in conventional CMOS technology. In this paper, we propose a method in which the numbers of transistors are significantly reduced. The related delay is extremely diminished, in the first glance we use this method to solve concerning problem of one decimal functional number some how this proposition can be extended to generalize the idea. Another advantage of this method is the independency on the kind of moduli.

Keywords: computer arithmetic, residue number system, number system, one-Hot, VLSI

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Authors: L. K. Davis

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The effects of the evolution force are observable in nature at all structural levels ranging from small molecular systems to conversely enormous biospheric systems. However, the evolution force and work associated with formation of biological structures has yet to be described mathematically or theoretically. In addressing the conundrum, we consider evolution from a unique perspective and in doing so we introduce the “Fundamental Theory of the Evolution Force: FTEF”. We utilized synthetic evolution artificial intelligence (SYN-AI) to identify genomic building blocks and to engineer 14-3-3 ζ docking proteins by transforming gene sequences into time-based DNA codes derived from protein hierarchical structural levels. The aforementioned served as templates for random DNA hybridizations and genetic assembly. The application of hierarchical DNA codes allowed us to fast forward evolution, while dampening the effect of point mutations. Natural selection was performed at each hierarchical structural level and mutations screened using Blosum 80 mutation frequency-based algorithms. Notably, SYN-AI engineered a set of three architecturally conserved docking proteins that retained motion and vibrational dynamics of native Bos taurus 14-3-3 ζ.

Keywords: 14-3-3 docking genes, synthetic protein design, time-based DNA codes, writing DNA code from scratch

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Authors: Matthew T. Wilson

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This paper covers a selection of research utilizing grammar-based genetic programming, and illustrates how context-free grammar can be used to constrain genetic programming. It focuses heavily on grammatical evolution, one of the most popular variants of grammar-based genetic programming, and the way its operators and terminals are specialized and modified from those in genetic programming. A variety of implementations of grammatical evolution for general use are covered, as well as research each focused on using grammatical evolution or grammar-based genetic programming on a single application, or to solve a specific problem, including some of the classically considered genetic programming problems, such as the Santa Fe Trail.

Keywords: context-free grammar, genetic algorithms, genetic programming, grammatical evolution

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Ismail Haddad, Djamel Herbadji, Aissa Belmeguenai, Selma Boumerdassi

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in this paper, we provide a novel approach for image encryption that employs the Fibonacci matrix and an enhanced fractional order chaotic map. The enhanced map overcomes the drawbacks of the classical map, especially the limited chaotic range and non-uniform distribution of chaotic sequences, resulting in a larger encryption key space. As a result, this strategy improves the encryption system's security. Our experimental results demonstrate that our proposed algorithm effectively encrypts grayscale images with exceptional efficiency. Furthermore, our technique is resistant to a wide range of potential attacks, including statistical and entropy attacks.

Keywords: image encryption, logistic map, fibonacci matrix, grayscale images

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Authors: Matevž Breška, Iztok Peruš, Vlado Stankovski

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Systematic overview of existing Ground Motion Prediction Equations (GMPEs) has been published by Douglas. The number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration (PGA) the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.

Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database, peak ground acceleration

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: Ceren Vardar Acar, Mine Caglar

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In finance, the price of a volatile asset can be modeled using fractional Brownian motion (fBm) with Hurst parameter H>1/2. The Black-Scholes model for the values of returns of an asset using fBm is given as, 〖Y_t=Y_0 e^((r+μ)t+σB)〗_t^H, 0≤t≤T where Y_0 is the initial value, r is constant interest rate, μ is constant drift and σ is constant diffusion coefficient of fBm, which is denoted by B_t^H where t≥0. Black-Scholes model can be constructed with some Markov processes such as Brownian motion. The advantage of modeling with fBm to Markov processes is its capability of exposing the dependence between returns. The real life data for a volatile asset display long-range dependence property. For this reason, using fBm is a more realistic model compared to Markov processes. Investors would be interested in any kind of information on the risk in order to manage it or hedge it. The maximum possible loss is one way to measure highest possible risk. Therefore, it is an important variable for investors. In our study, we give some theoretical bounds on the distribution of maximum possible loss of fBm. We provide both asymptotical and strong estimates for the tail probability of maximum loss of standard fBm and fBm with drift and diffusion coefficients. In the investment point of view, these results explain, how large values of possible loss behave and its bounds.

Keywords: maximum drawdown, maximum loss, fractional brownian motion, large deviation, Gaussian process

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Kayode Oshinubi, Brice Kammegne, Jacques Demongeot

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The use of mathematical tools like Partial Differential Equations and Ordinary Differential Equations have become very important to predict the evolution of a viral disease in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China causing a severe and potentially fatal respiratory syndrome, i.e., COVID-19. Since then, it has become a pandemic declared by World Health Organization (WHO) on March 11, 2020 which has spread around the globe. A reaction-diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process in which different substances are transformed, and a diffusion process that causes a distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined using the Lyapunov function are considered and the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. Also, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We showed the spatial distribution of the model compartments when the basic reproduction rate $\mathcal{R}_0 < 1$ and $\mathcal{R}_0 > 1$ and sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations. We investigate the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. To the public health policymakers, we offered a better understanding of the COVID-19 management.

Keywords: COVID-19, SEIRV epidemic model, reaction-diffusion equation, basic reproduction number, vaccination, spatial distribution

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Authors: Xue Xiao, Sun Hao, Liu Donghua

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E-commerce is experiencing rapid development and evolution, but traditional research methods are difficult to fully demonstrate the relationship between micro factors and macro evolution in the development process of e-commerce, which cannot provide accurate assessment for the existing strategies and predict the future evolution trends. To solve these problems, this paper presents the concept of e-commerce service ecosystem based on the characteristics of e-commerce and business ecosystem theory, describes e-commerce environment as a complex adaptive system from the perspective of ecology, constructs a e-commerce service ecosystem model by using Agent-based modeling method and Java language in RePast simulation platform and conduct experiment through the way of computational experiment, attempt to provide a suitable and effective researching method for the research on e-commerce evolution. By two experiments, it can be found that system model built in this paper is able to show the evolution process of e-commerce service ecosystem and the relationship between micro factors and macro emergence. Therefore, the system model constructed by Agent-based method and computational experiment provides proper means to study the evolution of e-commerce ecosystem.

Keywords: e-commerce service ecosystem, complex system, agent-based modeling, computational experiment

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Authors: Guram Adamashvili

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Surface plasmon polariton is a surface optical wave which undergoes a strong enhancement and spatial confinement of its wave amplitude near an interface of two-dimensional layered structures. Phosphorene (single-layer black phosphorus) and other two-dimensional anisotropic phosphorene-like materials are recognized as promising materials for potential future applications of surface plasmon polariton. A theory of an optical breather of self-induced transparency for surface plasmon polariton propagating in monolayer or few-layer phosphorene is developed. A theory of an optical soliton of self-induced transparency for surface plasmon polariton propagating in monolayer or few-layer phosphorene have been investigated earlier Starting from the optical nonlinear wave equation for surface TM-modes interacting with a two-dimensional layer of atomic systems or semiconductor quantum dots and a phosphorene monolayer (or other two-dimensional anisotropic material), we have obtained the evolution equations for the electric field of the breather. In this case, one finds that the evolution of these pulses become described by the damped Bloch-Maxwell equations. For surface plasmon polariton fields, breathers are found to occur. Explicit relations of the dependence of breathers on the local media, phosphorene anisotropic conductivity, transition layer properties and transverse structures of the SPP, are obtained and will be given. It is shown that the phosphorene conductivity reduces exponentially the amplitude of the surface breather of SIT in the process of propagation. The direction of propagation corresponding to the maximum and minimum damping of the amplitude are assigned along the armchair and zigzag directions of black phosphorus nano-film, respectively. The most rapid damping of the intensity occurs when the polarization of breather is along the armchair direction.

Keywords: breathers, nonlinear waves, solitons, surface plasmon polaritons

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Authors: Majid Karimabadi, Ahmad Farzaneh Kore, Behnam Azadegan

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The evolution of magnetized quark gluon plasma (QGP) in the framework of magneto- hydrodynamics is the focus of our study. We are investigating the temporal and spatial evolution of QGP using a second order viscous hydrodynamic framework. The fluid is considered to be magnetized and subjected to the influence of a magnetic field that is generated during the early stages of relativistic heavy ion collisions. We assume boost invariance along the beam line, which is represented by the z coordinate, and fluid expansion in the x direction. Additionally, we assume that the magnetic field is perpendicular to the reaction plane, which corresponds to the y direction. The fluid is considered to have infinite electrical conductivity. To analyze this system, we solve the coupled Maxwell and conservation equations. By doing so, we are able to determine the time and space dependence of the energy density, velocity, and magnetic field in the transverse plane of the viscous magnetized hot plasma. Furthermore, we obtain the spectrum of hadrons and compare it with experimental data.

Keywords: QGP, magnetohydrodynamics, hadrons, conversation

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: S. Ravichandra, D. V. L. N. Somayajulu

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Requirement of stakeholders for adding more details to the database is the main cause of the schema evolution in the relational database. Further, this schema evolution causes the instability to the database. Hence, it is aimed to define a metric suite for schema evolution of a relational database. The metric suite will calculate the metrics based on the features of the database, analyse the queries on the database and measures the coupling, cohesion and component dependencies of the schema for existing and evolved versions of the database. This metric suite will also provide an indicator for the problems related to the stability and usability of the evolved database. The degree of change in the schema of a database is presented in the forms of graphs that acts as an indicator and also provides the relations between various parameters (metrics) related to the database architecture. The acquired information is used to defend and improve the stability of database architecture. The challenges arise in incorporating these metrics with varying parameters for formulating a suitable metric suite are discussed. To validate the proposed metric suite, an experimentation has been performed on publicly available datasets.

Keywords: cohesion, coupling, entropy, metric suite, schema evolution

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Authors: Ranjith Maniyeri, Ahamed C. Saleel

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Two-dimensional fluid flow over a stationary circular cylinder is one of the bench mark problem in the field of fluid-structure interaction in computational fluid dynamics (CFD). Motivated by this, in the present work, a two-dimensional computational model is developed using an improved version of immersed boundary method which combines the feedback forcing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Lagrangian coordinates are used to represent the cylinder and Eulerian coordinates are used to describe the fluid flow. A two-dimensional Dirac delta function is used to transfer the quantities between the sold to fluid domain. Further, continuity and momentum equations governing the fluid flow are solved using fractional step based finite volume method on a staggered Cartesian grid system. The developed code is validated by comparing the values of drag coefficient obtained for different Reynolds numbers with that of other researcher’s results. Also, through numerical simulations for different Reynolds numbers flow behavior is well captured. The stability analysis of the improved version of immersed boundary method is tested for different values of feedback forcing coefficients.

Keywords: Feedback Forcing Scheme, Finite Volume Method, Immersed Boundary Method, Navier-Stokes Equations

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Authors: Antonios Katsianis

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I present the evolution of the galaxy Star Formation Rate Function (SFRF), star formation rate-stellar mass relation (SFR-M*) and Cosmic Star Formation Rate Density (CSFRD) of z = 0-8 galaxies employing both the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulations and a compilation of UV, Ha, radio and IR data. While I present comparisons between the above, I evaluate the effect and importance of supernovae/active galactic nuclei feedback. The relation between the star formation rate and stellar mass of galaxies represents a fundamental constraint on galaxy formation, and has been studied extensively both in observations and cosmological hydrodynamic simulations. However, a tension between the above is reported in the literature. I present the evolution of the SFR-M* relation and demonstrate the inconsistencies between observations that are retrieved using different methods. I employ cosmological hydrodynamic simulations combined with radiative transfer methods and compare these with a range of observed data in order to investigate further the root of this tension. Last, I present insights about the scatter of the SFR-M* relation and investigate which mechanisms (e.g. feedback) drive its shape and evolution.

Keywords: cosmological simulations, galaxy formation and evolution, star formation rate, stellar masses

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Authors: Minas Balyan

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Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

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In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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