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29 results for “nonlinear differential equations”
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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 abstractFREE CONVECTION OF HEAT TRANSFER IN FLOW PAST A SEMI-INFINITE FLAT PLATE IN TRANSVERSE MAGNETIC FIELD WITH HEAT FLUXP. Geetha, M.B.K. Moorthy, M. DakshinamoorthyA steady two-dimensional MHD free convection of heat transfer in flow past a semi-infinite flat plate in transverse magnetic field with heat flux has been examined. The governing partial differential equation are non-dimensionalised and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable η and using Runge-Kutta Gill method with shooting technique. The velocity … …American Journal of Applied Sciences, Vol. 11, Issue 9 · 4 Jul 2014 · 7,059 accessesView PDFCite
Research ArticleOpen accessIn the abstractDynamics of Coherent Structures in the Coupled Complex Ginzburg-Landau EquationsTat-Leung YeeProblem statement: In this study, we study the analytical construction of some exact solutions of a system of coupled physical differential equations, namely, the Complex Ginzburg-Landau Equations (CGLEs). CGLEs are intensively studied models of pattern formation in nonlinear dissipative media, with applications to biology, hydrodynamics, nonlinear optics, plasma physics, reaction-diffusion systems and many other fields. Approach: A system of two … …Journal of Mathematics and Statistics, Vol. 8, Issue 3 · 6 Nov 2012 · 6,990 accessesView PDFCite
Research ArticleOpen accessIn the abstractOn 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 abstractA 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 abstractNew Family of Exact Soliton Solutions for the Nonlinear Three-Wave Interaction EquationsSahar M. Alqaraleh, Adeeb G. TalafhaProblem statement: To obtain new exact traveling wave soliton solutions for the threewave interaction equation in a dispersive medium and a non zero phase mismatch. Approach: The tanh method is usually used to find a traveling wave analytic soliton solutions for one nonlinear wave and evolution partial differential equation. Here, we generalize this method to solve a system of nonlinear … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 31 Jan 2011 · 7,426 accessesView PDFCite
Research ArticleOpen accessIn the abstractVariational Homotopy Perturbation Method for the Zakharove-Kuznetsov EquationsMashaallah Matinfar, Maryam GhasemiProblem statement: In this research, the Variational Homotopy Perturbation Method (VHPM) which is a combination of Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM) used for the Zakharove-Kuznetsov equations (ZK-equations). Approach: These two methods are proposed by chinese researcher J.H.He. M.A.Noor improved these two methods and established the VHPM. The numerical solution of ZK-equation is of great importance dut … …Journal of Mathematics and Statistics, Vol. 6, Issue 4 · 24 Dec 2010 · 7,254 accessesView PDFCite
Research ArticleOpen accessIn the abstractApproximate Solutions of a Higher Order MHD Flow of a Uniformly Stretched Vertical Permeable Surface in the Presence of Heat Generation/Absorption which Resulted from a Quadratic ReactionO. K. KorikoHigher order MHD flow of a uniformity stretched vertical permeable surface in the presence of heat generation/absorption which resulted from a quadratic reaction was studied. The resulting coupled nonlinear partial differential equations is solved by asymptotic expansion. It was discovered that the maximum value of velocity occurs in the body of the fluid close to the surface not at the … …Journal of Mathematics and Statistics, Vol. 6, Issue 2 · 30 Jun 2010 · 7,445 accessesView PDFCite
Research ArticleOpen accessIn the abstractA Multiderivative Collocation Method for 5th Order Ordinary Differential EquationsS. J. Kayode, D. O. AwoyemiProblem statement: The conventional methods of solving higher order differential equations have been by reducing them to systems of first order equations. This approach is cumbersome and increases computational time. Approach: To address this problem, a numerical algorithm for direct solution of 5th order initial value problems in ordinary differential equations (odes), using power series as basis function, is proposed … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 8,928 accessesView PDFCite
Research ArticleOpen accessIn the abstractMathematical Model of Double Pass Photovoltaic Thermal Air Collector with FinsEbrahim M. Ali Alfegi, Kamaruzzaman Sopian, Mohd Yusof Hj Othman, Baharudin Bin YatimProblem statement: The efficiency of photovoltaic cells is generally temperature dependent (efficiency decrease when the temperature of the photovoltaic cells increase). This problem can be solved by cooling the solar cells during operation and operated at low temperature. Approach: This study presented a numerical model of double pass Photovoltaic Thermal (PV/T) solar air collector with fins attached to the back … …American Journal of Environmental Sciences, Vol. 5, Issue 5 · 31 Oct 2009 · 8,006 accessesView PDFCite