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14 articles for “differential transformation”
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Research ArticleOpen accessPhrase in the titleEfficiency of Differential Transformation Method for Genesio SystemJafar Husni AhmadProblem statement: In this study, a continuous solution for Genesio system was considered using Differential Transformation Method (DTM). Approach: Numerical results were compared to those obtained by the Runge-Kutta method to evaluate the performance of the suggested method. Results: The accuracy of the DTM was tested as the chaotic Genesio system. Conclusion/Recommendations: It was shown that the DTM was robust, … …Journal of Mathematics and Statistics, Vol. 5, Issue 2 · 30 Jun 2009 · 7,272 accessesView PDFCite
Research ArticleOpen accessIn the keywordsIntegrability and Prolongation Structure of a Generalized Korteweg-de Vries EquationPaul BrackenA closed differential ideal is constructed for a generalized Korteweg-de Vries equation. The ideal can be used to establish integrability for the equation. Some prolongation structures are determined for the equation and some larger prolongation algebras for given instances of the equation are found. The significance of this is that Backlund transformations can be developed based on them. It is … …Journal of Mathematics and Statistics, Vol. 6, Issue 2 · 30 Jun 2010 · 7,411 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn the Closed Form Solutions of Linear and Nonlinear Cauchy Reaction-Diffusion Equations Using the Hybrid of Fourier Transform and Variational Iteration MethodS.S. Nourazar, A. Nazari-Golshan, M. NourazarProblem statement: In the present study, a hybrid of Fourier transform and Variational Iteration Method (FTVIM) is developed for solving the non-homogeneous linear and nonlinear partial differential equations of Cauchy reaction-diffusion problem. Approach: The closed form solutions obtained from the series solution of recursive sequences is valid for the entire range of problem domain. Results and Conclusion: Moreover, the very … …Physics International, Vol. 2, Issue 1 · 26 Oct 2011 · 8,195 accessesView PDFCite
Research ArticleOpen accessIn the keywordsA New Perturbative Approach in Nonlinear Singularity AnalysisTat-Leung YeeProblem statement: The study is devoted to the “mirror” method which enables one to study the integrability of nonlinear differential equations. Approach: A perturbative extension of the mirror method is introduced. Results: The mirror system and its first perturbation are then utilized to gain insights into certain nonlinear equations possessing negative Fuchs indices, which were poorly understood in the literatures. … …Journal of Mathematics and Statistics, Vol. 7, Issue 3 · 29 Jul 2011 · 7,331 accessesView PDFCite
Research ArticleOpen accessIn the abstractGeometrical and Physical Effects on the Instability of a Fluid-Conveying PipeDahmane Mouloud, Samir Zahaf, Benkhettab Mohamed et al.The endeavor of this paper is to calculate frequencies and critical velocity of pipe carrying incompressible fluid are obtained using standard finite element method. Finite element beam type with two degrees of freedom per node was used. The natural frequencies of our system are calculated by using a program developed on MATLAB. The results are compared with those predicted by … …Current Research in Bioinformatics, Vol. 9, Issue 1 · 2 Nov 2020 · 11,324 accessesView PDFCite
Research ArticleOpen accessIn the abstractPhysical and Geometrical Effects on the Vibratory Pattern of a Pipe Carrying Fluid FlowDahmane Mouloud, Samir Zahaf, Mawhoub Soubih et al.In this research, the first natural frequencies and critical velocities of a fluid flow-conveying pipe are obtained with finite element method. By discretizing the structure wall and fluid flow, starting from beam type with two degrees of freedom per node. We determine the equation of motion from the fluid-structure coupling using Lagrange energy principle. Parameters frequencies and critical velocity of … …Current Research in Bioinformatics, Vol. 9, Issue 1 · 22 Oct 2020 · 11,396 accessesView PDFCite
Research ArticleOpen accessIn the abstractSolutions of the Duffing and Painlevé-Gambier Equations by Generalized Sundman TransformationDamien Kolawolé Kêgnidé Adjaï, Lucas Hervé Koudahoun, Jean Akande et al.A new approach using the generalized Sundman transformation to solve explicitly and exactly in a straightforward manner the cubic elliptic Duffing equation is proposed in this study. The method has the advantage to closely relate this equation to the linear harmonic oscillator equation and to be applied to solve other nonlinear differential equations. As a result, explicit and exact general … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 8 Nov 2018 · 7,251 accessesView PDFCite
Research ArticleOpen accessIn the abstractTheory 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 accessIn the abstractExact Classical and Quantum Mechanics of a Generalized Singular Equation of Quadratic Liénard TypeLucas H. Koudahoun, Jean Akande, Damien K.K. Adjaï et al.Authors introduce a generalized singular differential equation of quadratic Liénard type for study of exact classical and quantum mechanical solutions. The equation is shown to exhibit periodic solutions and to include the linear harmonic oscillator equation and the Painlevé-Gambier XVII equation as special cases. It is also shown that the equation may exhibit discrete eigenstates as quantum behavior under Nikiforov-Uvarov … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 5 Jul 2018 · 7,609 accessesView PDFCite
Research ArticleOpen accessIn the abstractTransient MHD Mixed Double Diffusive Convection Along a Vertical Plate Embedded in a Non-Darcy Porous Medium with Suction or InjectionKhaled K. JaberProblem statement: Transient non-Darcy mixed double convection from a semi-infinite, isothermal vertical plate embedded in a homogeneous porous medium, in the presence of surface suction or injection had been numerically investigated. Approach: Forchheimer extension was considered in the flow equations. Appropriate transformations were employed to transform the derived partial differential equations governing the problem under consideration on the assumption of … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 10 Dec 2011 · 7,121 accessesView PDFCite