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13 articles for “Nonlinear Partial Differential Equations”
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Research ArticleOpen accessEvery word in the titleA New Approach to Solve Nonlinear Partial Differential EquationsAbdoul R. Ghotbi, M. A. Mohammadzade, A. Avaei, M. KeyvanipoorNonlinear phenomena play a crucial role in applied mathematics and physics. Explicit solutions to the nonlinear equations are of fundamental importance. Various methods for obtaining explicit solution to nonlinear evolution equations have been proposed. In this letter homotopy perturbation method (HPM) is employed for solving one-dimensional non-homogeneous parabolic partial differential equation with a variable coefficient and a system of nonlinear … …Journal of Mathematics and Statistics, Vol. 3, Issue 4 · 31 Dec 2007 · 6,916 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Regularity of the Solutions to the Cauchy Problem for the Quasilinear Second-Order Parabolic Partial Differential EquationsMykola YaremenkoThis article is dedicated to expanding our comprehension of the regularity of the solutions to the Cauchy problem for the quasilinear second-order parabolic partial differential equations under fair general conditions on the nonlinear perturbations. In this paper have been obtained that the sequence of the weak solutions uz ∈ V1,02, z = 1,2,..... to the Cauchy problems for the Equations … …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 2 Jun 2020 · 7,282 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 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 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 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
Research ArticleOpen accessIn the abstractHomotopy Perturbation Method and Variational Iteration Method for Solving Zakharov-Kuznetsov EquationB. Ganjavi, H. Mohammadi, D.D. Ganji, A. BarariThis article investigates a nonlinear dispersive Zakharov-Kuznetsov ZK (3, 3, 3) equation. This equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) are implemented for solving the ZK equation. Homotopy results were compared with … …American Journal of Applied Sciences, Vol. 5, Issue 7 · 31 Jul 2008 · 6,798 accessesView PDFCite
Research ArticleOpen accessAll words, across the recordApproximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform MethodEman Abuteen, Asad Freihat, Mohammed Al-Smadi et al.This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different … …Journal of Mathematics and Statistics, Vol. 12, Issue 1 · 26 Mar 2016 · 7,901 accessesView PDFCite