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integral equations</title> <meta name="description" content="Search results for: nonlinear integral equations"> <meta name="keywords" content="nonlinear integral equations"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="nonlinear integral equations"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 3580</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: nonlinear integral equations</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3580</span> The Finite Element Method for Nonlinear Fredholm Integral Equation of the Second Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Melusi%20Khumalo">Melusi Khumalo</a>, <a href="https://publications.waset.org/abstracts/search?q=Anastacia%20Dlamini"> Anastacia Dlamini</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title="finite element method">finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20approach" title=" Galerkin approach"> Galerkin approach</a>, <a href="https://publications.waset.org/abstracts/search?q=Fredholm%20integral%20equations" title=" Fredholm integral equations"> Fredholm integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20integral%20equations" title=" nonlinear integral equations"> nonlinear integral equations</a> </p> <a href="https://publications.waset.org/abstracts/140832/the-finite-element-method-for-nonlinear-fredholm-integral-equation-of-the-second-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140832.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">376</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3579</span> X-Ray Dynamical Diffraction 'Third Order Nonlinear Renninger Effect'</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Minas%20Balyan">Minas Balyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bragg%20diffraction" title="Bragg diffraction">Bragg diffraction</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Takagi%E2%80%99s%20equations" title=" nonlinear Takagi’s equations"> nonlinear Takagi’s equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Renninger%20effect" title=" nonlinear Renninger effect"> nonlinear Renninger effect</a>, <a href="https://publications.waset.org/abstracts/search?q=third%20order%20nonlinearity" title=" third order nonlinearity"> third order nonlinearity</a> </p> <a href="https://publications.waset.org/abstracts/55035/x-ray-dynamical-diffraction-third-order-nonlinear-renninger-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55035.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">385</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3578</span> Integral Image-Based Differential Filters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kohei%20Inoue">Kohei Inoue</a>, <a href="https://publications.waset.org/abstracts/search?q=Kenji%20Hara"> Kenji Hara</a>, <a href="https://publications.waset.org/abstracts/search?q=Kiichi%20Urahama"> Kiichi Urahama</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integral%20images" title="integral images">integral images</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20images" title=" differential images"> differential images</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20filters" title=" differential filters"> differential filters</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20fusion" title=" image fusion"> image fusion</a> </p> <a href="https://publications.waset.org/abstracts/8531/integral-image-based-differential-filters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8531.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">506</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3577</span> Numerical Solutions of Fredholm Integral Equations by B-Spline Wavelet Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ritu%20Rani">Ritu Rani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=semi-orthogonal" title="semi-orthogonal">semi-orthogonal</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20arrangement" title=" wavelet arrangement"> wavelet arrangement</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equations" title=" integral equations"> integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20development" title=" wavelet development "> wavelet development </a> </p> <a href="https://publications.waset.org/abstracts/125473/numerical-solutions-of-fredholm-integral-equations-by-b-spline-wavelet-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125473.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">174</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3576</span> Further Results on Modified Variational Iteration Method for the Analytical Solution of Nonlinear Advection Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20W.%20Gbolagade">A. W. Gbolagade</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20O.%20Olayiwola"> M. O. Olayiwola</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20O.%20Kareem"> K. O. Kareem</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lagrange%20multiplier" title="lagrange multiplier">lagrange multiplier</a>, <a href="https://publications.waset.org/abstracts/search?q=non-homogeneous%20equations" title=" non-homogeneous equations"> non-homogeneous equations</a>, <a href="https://publications.waset.org/abstracts/search?q=advection%20equations" title=" advection equations"> advection equations</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematics" title=" mathematics"> mathematics</a> </p> <a href="https://publications.waset.org/abstracts/3945/further-results-on-modified-variational-iteration-method-for-the-analytical-solution-of-nonlinear-advection-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3945.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">301</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3575</span> Numerical Solution of Integral Equations by Using Discrete GHM Multiwavelet</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Archit%20Yajnik">Archit Yajnik</a>, <a href="https://publications.waset.org/abstracts/search?q=Rustam%20Ali"> Rustam Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=GHM%20multiwavelet" title="GHM multiwavelet">GHM multiwavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=fredholm%20integral%20equations" title=" fredholm integral equations"> fredholm integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=quadrature%20method" title=" quadrature method"> quadrature method</a>, <a href="https://publications.waset.org/abstracts/search?q=function%20approximation" title=" function approximation"> function approximation</a> </p> <a href="https://publications.waset.org/abstracts/36311/numerical-solution-of-integral-equations-by-using-discrete-ghm-multiwavelet" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36311.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">462</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3574</span> Numerical Iteration Method to Find New Formulas for Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kholod%20Mohammad%20Abualnaja">Kholod Mohammad Abualnaja</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=variational%20iteration%20method" title="variational iteration method">variational iteration method</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20equations" title=" nonlinear equations"> nonlinear equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Lagrange%20multiplier" title=" Lagrange multiplier"> Lagrange multiplier</a>, <a href="https://publications.waset.org/abstracts/search?q=algorithms" title=" algorithms "> algorithms </a> </p> <a href="https://publications.waset.org/abstracts/12184/numerical-iteration-method-to-find-new-formulas-for-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12184.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">545</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3573</span> Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Leila%20Motamed-Jahromi">Leila Motamed-Jahromi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohsen%20Hatami"> Mohsen Hatami</a>, <a href="https://publications.waset.org/abstracts/search?q=Alireza%20Keshavarz"> Alireza Keshavarz </a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As<sub>2</sub>S<sub>3</sub> 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<span dir="RTL">.</span> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20optics" title="nonlinear optics">nonlinear optics</a>, <a href="https://publications.waset.org/abstracts/search?q=plasmonic%20waveguide" title=" plasmonic waveguide"> plasmonic waveguide</a>, <a href="https://publications.waset.org/abstracts/search?q=chalcogenide" title=" chalcogenide"> chalcogenide</a>, <a href="https://publications.waset.org/abstracts/search?q=propagation%20equation" title=" propagation equation"> propagation equation</a> </p> <a href="https://publications.waset.org/abstracts/52758/equations-of-pulse-propagation-in-three-layer-structure-of-as2s3-chalcogenide-plasmonic-nano-waveguides" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52758.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">418</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3572</span> Integrable Heisenberg Ferromagnet Equations with Self-Consistent Potentials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gulgassyl%20Nugmanova">Gulgassyl Nugmanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhanat%20Zhunussova"> Zhanat Zhunussova</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuralay%20Yesmakhanova"> Kuralay Yesmakhanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Galya%20Mamyrbekova"> Galya Mamyrbekova</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratbay%20Myrzakulov"> Ratbay Myrzakulov </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Heisenberg%20Ferromagnet%20equations" title="Heisenberg Ferromagnet equations">Heisenberg Ferromagnet equations</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20equations" title=" soliton equations"> soliton equations</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalence" title=" equivalence"> equivalence</a>, <a href="https://publications.waset.org/abstracts/search?q=Lax%20representation" title=" Lax representation"> Lax representation</a> </p> <a href="https://publications.waset.org/abstracts/27440/integrable-heisenberg-ferromagnet-equations-with-self-consistent-potentials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27440.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">457</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3571</span> Research of Amplitude-Frequency Characteristics of Nonlinear Oscillations of the Interface of Two-Layered Liquid</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Win%20Ko%20Ko">Win Ko Ko</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20N.%20Temnov"> A. N. Temnov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20oscillations" title="nonlinear oscillations">nonlinear oscillations</a>, <a href="https://publications.waset.org/abstracts/search?q=two-layered%20liquid" title=" two-layered liquid"> two-layered liquid</a>, <a href="https://publications.waset.org/abstracts/search?q=instability%20region" title=" instability region"> instability region</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrodynamic%20coefficients" title=" hydrodynamic coefficients"> hydrodynamic coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=resonance%20frequency" title=" resonance frequency"> resonance frequency</a> </p> <a href="https://publications.waset.org/abstracts/115967/research-of-amplitude-frequency-characteristics-of-nonlinear-oscillations-of-the-interface-of-two-layered-liquid" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/115967.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">219</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3570</span> A Coupled System of Caputo-Type Katugampola Fractional Differential Equations with Integral Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yacine%20Arioua">Yacine Arioua</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20differential%20equations" title="fractional differential equations">fractional differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=coupled%20system" title=" coupled system"> coupled system</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo-Katugampola%20derivative" title=" Caputo-Katugampola derivative"> Caputo-Katugampola derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point%20theorems" title=" fixed point theorems"> fixed point theorems</a>, <a href="https://publications.waset.org/abstracts/search?q=existence" title=" existence"> existence</a>, <a href="https://publications.waset.org/abstracts/search?q=uniqueness" title=" uniqueness"> uniqueness</a> </p> <a href="https://publications.waset.org/abstracts/124953/a-coupled-system-of-caputo-type-katugampola-fractional-differential-equations-with-integral-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124953.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">264</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3569</span> On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Giniatoulline">A. Giniatoulline</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20method" title="Galerkin method">Galerkin method</a>, <a href="https://publications.waset.org/abstracts/search?q=Navier-Stokes%20equations" title=" Navier-Stokes equations"> Navier-Stokes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20partial%20differential%20equations" title=" nonlinear partial differential equations"> nonlinear partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Sobolev%20spaces" title=" Sobolev spaces"> Sobolev spaces</a>, <a href="https://publications.waset.org/abstracts/search?q=stratified%20fluid" title=" stratified fluid"> stratified fluid</a> </p> <a href="https://publications.waset.org/abstracts/52024/on-the-strong-solutions-of-the-nonlinear-viscous-rotating-stratified-fluid" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52024.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">309</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3568</span> Numerical Wave Solutions for Nonlinear Coupled Equations Using Sinc-Collocation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nonlinear%20coupled%20KdV%20equations" title="Nonlinear coupled KdV equations">Nonlinear coupled KdV equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Soliton%20solutions" title=" Soliton solutions"> Soliton solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Sinc-collocation%20method" title=" Sinc-collocation method"> Sinc-collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Sinc%20functions" title=" Sinc functions"> Sinc functions</a> </p> <a href="https://publications.waset.org/abstracts/23564/numerical-wave-solutions-for-nonlinear-coupled-equations-using-sinc-collocation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23564.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">524</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3567</span> The Application of Variable Coefficient Jacobian elliptic Function Method to Differential-Difference Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chao-Qing%20Dai">Chao-Qing Dai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20sine-Gordon%20equation" title="discrete sine-Gordon equation">discrete sine-Gordon equation</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20coefficient%20Jacobian%20elliptic%20function%20method" title=" variable coefficient Jacobian elliptic function method"> variable coefficient Jacobian elliptic function method</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=equation" title=" equation"> equation</a> </p> <a href="https://publications.waset.org/abstracts/12987/the-application-of-variable-coefficient-jacobian-elliptic-function-method-to-differential-difference-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12987.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">668</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3566</span> Nonlinear Equations with n-Dimensional Telegraph Operator Iterated K-Times</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jessada%20Tariboon">Jessada Tariboon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=telegraph%20operator" title="telegraph operator">telegraph operator</a>, <a href="https://publications.waset.org/abstracts/search?q=elementary%20solution" title=" elementary solution"> elementary solution</a>, <a href="https://publications.waset.org/abstracts/search?q=distribution%20kernel" title=" distribution kernel"> distribution kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20equations" title=" nonlinear equations"> nonlinear equations</a> </p> <a href="https://publications.waset.org/abstracts/5031/nonlinear-equations-with-n-dimensional-telegraph-operator-iterated-k-times" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5031.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">489</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3565</span> X-Ray Dynamical Diffraction Rocking Curves in Case of Third Order Nonlinear Renninger Effect</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Minas%20Balyan">Minas Balyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the third-order nonlinear Takagi’s equations for monochromatic waves and in the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses for forbidden reflections the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero. 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 and numerically. If the reflection exactly is forbidden the diffracted wave’s amplitude is zero both in Laue and Bragg cases since the boundary conditions and dynamical diffraction equations are compatible with zero solution. But in real crystals due to some percent of dislocations and other localized defects, the atoms are displaced with respect to their equilibrium positions. Thus in real crystals susceptibilities of forbidden reflection are by some order small than for usual not forbidden reflections but are not exactly equal to zero. The numerical calculations for susceptibilities two order less than for not forbidden reflection show that in Bragg geometry case the nonlinear reflection curve’s behavior is the same as for not forbidden reflection, but for forbidden reflection the rocking curves’ width, center and boundaries are two order sensitive on the input intensity value. This gives an opportunity to investigate third order nonlinear X-ray dynamical diffraction for not intense beams – 0.001 in the units of critical intensity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=third%20order%20nonlinearity" title="third order nonlinearity">third order nonlinearity</a>, <a href="https://publications.waset.org/abstracts/search?q=Bragg%20diffraction" title=" Bragg diffraction"> Bragg diffraction</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Renninger%20effect" title=" nonlinear Renninger effect"> nonlinear Renninger effect</a>, <a href="https://publications.waset.org/abstracts/search?q=rocking%20curves" title=" rocking curves"> rocking curves</a> </p> <a href="https://publications.waset.org/abstracts/56984/x-ray-dynamical-diffraction-rocking-curves-in-case-of-third-order-nonlinear-renninger-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56984.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">406</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3564</span> Analytical Solving of Nonlinear Differential Equations in the Nonlinear Phenomena for Viscos Fluids </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arash%20Jafari">Arash Jafari</a>, <a href="https://publications.waset.org/abstracts/search?q=Mehdi%20Taghaddosi"> Mehdi Taghaddosi</a>, <a href="https://publications.waset.org/abstracts/search?q=Azin%20Parvin"> Azin Parvin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=viscos%20fluid" title="viscos fluid">viscos fluid</a>, <a href="https://publications.waset.org/abstracts/search?q=incompressible%20fluid%20flow" title=" incompressible fluid flow"> incompressible fluid flow</a>, <a href="https://publications.waset.org/abstracts/search?q=inclined%20plane" title=" inclined plane"> inclined plane</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20phenomena" title=" nonlinear phenomena"> nonlinear phenomena</a> </p> <a href="https://publications.waset.org/abstracts/58352/analytical-solving-of-nonlinear-differential-equations-in-the-nonlinear-phenomena-for-viscos-fluids" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58352.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">283</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3563</span> A Multistep Broyden’s-Type Method for Solving Systems of Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Y.%20Waziri">M. Y. Waziri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20Aliyu"> M. A. Aliyu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mulit-step%20Broyden" title="mulit-step Broyden">mulit-step Broyden</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems%20of%20equations" title=" nonlinear systems of equations"> nonlinear systems of equations</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20efficiency" title=" computational efficiency"> computational efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=iterate" title=" iterate"> iterate</a> </p> <a href="https://publications.waset.org/abstracts/13750/a-multistep-broydens-type-method-for-solving-systems-of-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13750.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">638</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3562</span> Global Stability Of Nonlinear Itô Equations And N. V. Azbelev's W-method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov.">Arcady Ponosov.</a>, <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20Kadiev"> Ramazan Kadiev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20stability" title="asymptotic stability">asymptotic stability</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title=" delay equations"> delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a> </p> <a href="https://publications.waset.org/abstracts/143260/global-stability-of-nonlinear-ito-equations-and-n-v-azbelevs-w-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/143260.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">224</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3561</span> Scrutiny and Solving Analytically Nonlinear Differential at Engineering Field of Fluids, Heat, Mass and Wave by New Method AGM</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammadreza%20Akbari">Mohammadreza Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Sara%20Akbari"> Sara Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Davood%20Domiri%20Ganji"> Davood Domiri Ganji</a>, <a href="https://publications.waset.org/abstracts/search?q=Pooya%20Solimani"> Pooya Solimani</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Khalili"> Reza Khalili</a> </p> <p class="card-text"><strong>Abstract:</strong></p> As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, 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 a 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 be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=new%20method%20AGM" title="new method AGM">new method AGM</a>, <a href="https://publications.waset.org/abstracts/search?q=sets%20of%20coupled%20nonlinear%20equations%20at%20engineering%20field" title=" sets of coupled nonlinear equations at engineering field"> sets of coupled nonlinear equations at engineering field</a>, <a href="https://publications.waset.org/abstracts/search?q=waves%20equations" title=" waves equations"> waves equations</a>, <a href="https://publications.waset.org/abstracts/search?q=integro-differential" title=" integro-differential"> integro-differential</a>, <a href="https://publications.waset.org/abstracts/search?q=fluid%20and%20thermal" title=" fluid and thermal"> fluid and thermal</a> </p> <a href="https://publications.waset.org/abstracts/36022/scrutiny-and-solving-analytically-nonlinear-differential-at-engineering-field-of-fluids-heat-mass-and-wave-by-new-method-agm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36022.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">546</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3560</span> Propagation of W Shaped of Solitons in Fiber Bragg Gratings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mezghiche%20Kamel">Mezghiche Kamel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the ﬁber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%EF%AC%81ber%20bragg%20grating" title="ﬁber bragg grating">ﬁber bragg grating</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear-coupled%20mode%20equations" title=" nonlinear-coupled mode equations"> nonlinear-coupled mode equations</a>, <a href="https://publications.waset.org/abstracts/search?q=w%20shaped%20of%20solitons" title=" w shaped of solitons"> w shaped of solitons</a>, <a href="https://publications.waset.org/abstracts/search?q=PNLS" title=" PNLS"> PNLS</a> </p> <a href="https://publications.waset.org/abstracts/12669/propagation-of-w-shaped-of-solitons-in-fiber-bragg-gratings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12669.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">769</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3559</span> Modified Newton's Iterative Method for Solving System of Nonlinear Equations in Two Variables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sara%20Mahesar">Sara Mahesar</a>, <a href="https://publications.waset.org/abstracts/search?q=Saleem%20M.%20Chandio"> Saleem M. Chandio</a>, <a href="https://publications.waset.org/abstracts/search?q=Hira%20Soomro"> Hira Soomro</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conventional%20Newton%E2%80%99s%20method" title="conventional Newton’s method">conventional Newton’s method</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20Newton%E2%80%99s%20method" title=" modified Newton’s method"> modified Newton’s method</a>, <a href="https://publications.waset.org/abstracts/search?q=order%20of%20convergence" title=" order of convergence"> order of convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=system%20of%20nonlinear%20equations" title=" system of nonlinear equations"> system of nonlinear equations</a> </p> <a href="https://publications.waset.org/abstracts/87602/modified-newtons-iterative-method-for-solving-system-of-nonlinear-equations-in-two-variables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/87602.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">257</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3558</span> Existence of positive periodic solutions for certain delay differential equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Farid%20Nouioua">Farid Nouioua</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelouaheb%20Ardjouni"> Abdelouaheb Ardjouni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20differential%20equations" title="delay differential equations">delay differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=positive%20periodic%20solutions" title=" positive periodic solutions"> positive periodic solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equations" title=" integral equations"> integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Krasnoselskii%20fixed%20point%20theorem" title=" Krasnoselskii fixed point theorem"> Krasnoselskii fixed point theorem</a> </p> <a href="https://publications.waset.org/abstracts/40904/existence-of-positive-periodic-solutions-for-certain-delay-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40904.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">438</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3557</span> On Deterministic Chaos: Disclosing the Missing Mathematics from the Lorenz-Haken Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meziane%20Belkacem">Meziane Belkacem</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Physics" title="Physics">Physics</a>, <a href="https://publications.waset.org/abstracts/search?q=optics" title=" optics"> optics</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20dynamics" title=" nonlinear dynamics"> nonlinear dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=chaos" title=" chaos"> chaos</a> </p> <a href="https://publications.waset.org/abstracts/140512/on-deterministic-chaos-disclosing-the-missing-mathematics-from-the-lorenz-haken-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140512.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">156</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3556</span> Investigate and Solving Analytic of Nonlinear Differential at Vibrations (Earthquake)and Beam-Column, by New Approach “AGM”</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammadreza%20Akbari">Mohammadreza Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Pooya%20Soleimani%20Besheli"> Pooya Soleimani Besheli</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Khalili"> Reza Khalili</a>, <a href="https://publications.waset.org/abstracts/search?q=Sara%20Akbari"> Sara Akbari </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=new%20method%20AGM" title="new method AGM">new method AGM</a>, <a href="https://publications.waset.org/abstracts/search?q=vibrations" title=" vibrations"> vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=beam-column" title=" beam-column"> beam-column</a>, <a href="https://publications.waset.org/abstracts/search?q=angular%20frequency" title=" angular frequency"> angular frequency</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20dissipated" title=" energy dissipated"> energy dissipated</a>, <a href="https://publications.waset.org/abstracts/search?q=critical%20load" title=" critical load"> critical load</a> </p> <a href="https://publications.waset.org/abstracts/33102/investigate-and-solving-analytic-of-nonlinear-differential-at-vibrations-earthquakeand-beam-column-by-new-approach-agm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33102.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">391</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3555</span> Weak Solutions Of Stochastic Fractional Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lev%20Idels">Lev Idels</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title="delay equations">delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solutions" title=" weak solutions"> weak solutions</a> </p> <a href="https://publications.waset.org/abstracts/146592/weak-solutions-of-stochastic-fractional-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146592.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3554</span> Nonlinear Free Vibrations of Functionally Graded Cylindrical Shells</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexandra%20Andrade%20Brand%C3%A3o%20Soares">Alexandra Andrade Brandão Soares</a>, <a href="https://publications.waset.org/abstracts/search?q=Paulo%20Batista%20Gon%C3%A7alves"> Paulo Batista Gonçalves</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cylindrical%20shells" title="cylindrical shells">cylindrical shells</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamics" title=" dynamics"> dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20material" title=" functionally graded material"> functionally graded material</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20vibrations" title=" nonlinear vibrations"> nonlinear vibrations</a> </p> <a href="https://publications.waset.org/abstracts/183404/nonlinear-free-vibrations-of-functionally-graded-cylindrical-shells" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/183404.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">65</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3553</span> Superconvergence of the Iterated Discrete Legendre Galerkin Method for Fredholm-Hammerstein Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Payel%20Das">Payel Das</a>, <a href="https://publications.waset.org/abstracts/search?q=Gnaneshwar%20Nelakanti"> Gnaneshwar Nelakanti</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hammerstein%20integral%20equations" title="hammerstein integral equations">hammerstein integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20galerkin" title=" discrete galerkin"> discrete galerkin</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%0D%0Aquadrature" title=" numerical quadrature"> numerical quadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=superconvergence" title=" superconvergence"> superconvergence</a> </p> <a href="https://publications.waset.org/abstracts/22260/superconvergence-of-the-iterated-discrete-legendre-galerkin-method-for-fredholm-hammerstein-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22260.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">471</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3552</span> Nonlinear Impact Responses for a Damped Frame Supported by Nonlinear Springs with Hysteresis Using Fast FEA</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20Yamaguchi">T. Yamaguchi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Watanabe"> M. Watanabe</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Sasajima"> M. Sasajima</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Yuan"> C. Yuan</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Maruyama"> S. Maruyama</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20B.%20Ibrahim"> T. B. Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20Tomita"> H. Tomita</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20response" title="dynamic response">dynamic response</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20impact%20response" title=" nonlinear impact response"> nonlinear impact response</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20analysis" title=" finite element analysis"> finite element analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20analysis" title=" numerical analysis"> numerical analysis</a> </p> <a href="https://publications.waset.org/abstracts/15947/nonlinear-impact-responses-for-a-damped-frame-supported-by-nonlinear-springs-with-hysteresis-using-fast-fea" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15947.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">434</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3551</span> Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Emad%20K.%20Jaradat">Emad K. Jaradat</a>, <a href="https://publications.waset.org/abstracts/search?q=Ala%E2%80%99a%20Al-Faqih"> Ala’a Al-Faqih</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20Schrodinger%20equation" title="non-linear Schrodinger equation">non-linear Schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Elzaki%20decomposition%20method" title=" Elzaki decomposition method"> Elzaki decomposition method</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20oscillator" title=" harmonic oscillator"> harmonic oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=one%20and%20two-dimensional%20Schrodinger%20equation" title=" one and two-dimensional Schrodinger equation"> one and two-dimensional Schrodinger equation</a> </p> <a 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