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Research ArticleOpen accessEvery word in the titleAnalytical Investigation of Hyperbolic Equations via He's MethodsD.D. Ganji, M. Amini, A. KolahdoozPerturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods were introduced to solve nonlinear heat transfer problems in this Letter, one is He's Variational Iteration Method (VIM) and the other is the Homotopy-Perturbation Method (HPM). Nonlinear hyperbolic equations were used as examples … …American Journal of Engineering and Applied Sciences, Vol. 1, Issue 4 · 31 Dec 2008 · 7,115 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleApproximate Analytical Solutions For Time-Dependent Emden-Fowler-Type Equations By Variational Iteration MethodKhaled BatihaThe main objective of the current study was to solve the time-dependent Emden-Fowler-type equation with singular behavior. The technique used here was called the variational iteration method (VIM). The advantage of this work is twofold. Firstly, the VIM reduces the computational work. Secondly, in comparison with existing techniques, the VIM is an improvement with regard to its accuracy and rapid … …American Journal of Applied Sciences, Vol. 4, Issue 7 · 31 Jul 2007 · 6,591 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleExistence Results for a Class of Nonlinear Hadamard Fractional with p-Laplacian Operator Differential EquationsSamah HorrigueIn this study, we are concerned with the existence and uniqueness of solution for some nonlinear Hadamard fractional differential equations. Our results are based on different classical fixed point theorems. Some useful examples are presented in order to illustrate the validity of our main results. …Journal of Mathematics and Statistics, Vol. 17, Issue 1 · 2 Oct 2021 · 6,886 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleMachine Motion Equations Presented in a New General FormatNicolae Petrescu, Florian Ion Tiberiu PetrescuConsidering the increased importance of robots nowadays, when no large factory or factory can work without robots, we want to present in the work the motion equations of the machine in an original form, both in terms of aspect and their deduction. The machine's motion equations can be used in dynamic calculations at any type of machine, whether it be … …Journal of Mechatronics and Robotics, Vol. 3, Issue 1 · 22 May 2019 · 6,131 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleTheory of Exact Trigonometric Periodic Solutions to Quadratic Liénard Type EquationsJean Akande, Damien Kolawolé Kêgnidé Adjaï, Marc Delphin MonsiaA mathematical theory is developed through generalized Sundman transformation to show the existence of classes of quadratic Liénard type equations which admit exact and explicit general trigonometric solutions but with amplitude-dependent frequency. The application of the theory to compute also exact and explicit general periodic solutions to nonlinear differential equations like inverted Painlevé-Gambier equations in terms of trigonometric or Jacobian … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 29 Oct 2018 · 7,215 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleOn Gröbner Bases and Their Uses in Solving System of Polynomial Equations and Graph ColoringHaridas Kumar Das, Nasim RezaThis paper is based on the analytic and computational solution procedures of Gröbner basis and its applications. We show the behavior of the ideals generated by polynomials from a polynomial ring. We also present the idea of a zero dimensional ideal and use of this ideal to solve system of polynomial equations. We then introduce an algorithmic procedure for solving … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 27 Jun 2018 · 8,591 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleStudy of Fractional Order Integro-Differential Equations by using Chebyshev Neural NetworkSarkhosh S. Chaharborj, Shahriar S. Chaharborj, Yaghoub MahmoudiRecently fractional integro-differential equations have been proposed for the modeling of many complex systems. Simulation of these equations requires the development of suitable numerical methods. This paper is devoted to finding the numerical solution of some classes of fractional integro-differential equations by employing the Chebyshev Neural Network (ChNN). The accuracy of proposed method is shown by comparing the numerical results … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 11 Feb 2017 · 7,403 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleExplicit Direct Integrators of RK Type for Solving Special Fifth-Order Ordinary Differential EquationsMohammed S. Mechee, Murtaza A. KadhimThe main contribution of this paper is the development of direct explicit methods of Runge-Kutta (RK) type for solving special fifth-Order Ordinary Differential Equations (ODEs). For this purpose, we have generalized RKD and RKT methods of special third and fourth-order ODEs. Using Taylor expansion, we have derived the algebraic equations of algebraic equations of order conditions for the proposed RKM … …American Journal of Applied Sciences, Vol. 13, Issue 12 · 26 Dec 2016 · 7,940 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleAdapted Newton-Kantorovich Methods for Nonlinear Integral EquationsMostefa Nadir, Amina KhiraniFor this work, the main idea is to make an adapted modification to the Newton-Kantorovich method destined to solve a nonlinear integral equations, so that by this technical method we obtain a simple application to this solution. Moreover, we compare the numerical results obtained by this method against ones obtained by another authors. This comparison showed the efficiency of this … …Journal of Mathematics and Statistics, Vol. 12, Issue 3 · 2 Jul 2016 · 7,294 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleSome Contributions to the Theory of Abstract Degenerate Volterra Integro-Differential EquationsMarko KostićIn this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equations with Caputo derivatives by using the pure Laplace transform techniques. …Journal of Mathematics and Statistics, Vol. 12, Issue 2 · 17 Jun 2016 · 7,406 accessesView PDFCite