Analytical solution of wave system in Rn with coupling controllers

Purpose – The purpose of this paper is to consider analytical solution of wave system in Rn with coupling controllers by using the homotopy perturbation method (HPM).Design/methodology/approach – HPM is applied to the system of linear partial differential equations, i.e. the system of waves in the two‐dimensional version of system equations (1) and (2). This problem is motivated by an analogous problem in ordinary differential equations for coupled oscillators and has potential application in isolating a vibrating object from the outside disturbances. For example, rubber or rubber‐like materials can be used to either absorb or shield a structure from vibration. As an approximation, these materials can be modeled as distributed springs.Findings – In this paper, HPM was used to obtain analytical solution of wave system in with coupling controllers. The method provides the solutions in the form of a series with easily computable terms. Unlike other common methods for solving any physical problem, linear or n...

[1]  Esmail Babolian,et al.  Some notes on using the homotopy perturbation method for solving time-dependent differential equations , 2009, Math. Comput. Model..

[2]  Livija Cveticanin,et al.  Homotopy–perturbation method for pure nonlinear differential equation , 2006 .

[3]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[4]  Mehdi Dehghan,et al.  Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method , 2007 .

[5]  Distributed and Boundary Control for a Parallel System of Euler-Bernoulli Beams , 1997 .

[6]  M. Dehghan,et al.  The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics , 2008 .

[7]  Ji-Huan He.  AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING , 2008 .

[8]  Ji-Huan He,et al.  Addendum:. New Interpretation of Homotopy Perturbation Method , 2006 .

[9]  M. Noor,et al.  Some Relatively New Techniques for Nonlinear Problems , 2009 .

[10]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[11]  Mehdi Dehghan,et al.  SOLUTION OF AN INTEGRO-DIFFERENTIAL EQUATION ARISING IN OSCILLATING MAGNETIC FIELDS USING HE'S HOMOTOPY PERTURBATION METHOD , 2008 .

[12]  Ji-Huan He.  New interpretation of homotopy perturbation method , 2006 .

[13]  Ji-Huan He.  A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[14]  M. Dehghan,et al.  Application of He’s homotopy perturbation method for non-linear system of second-order boundary value problems , 2009 .

[15]  Muhammad Aslam Noor,et al.  Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems , 2007 .

[16]  K. Omrani,et al.  Application of the homotopy perturbation method to the modified regularized long‐wave equation , 2010 .

[17]  Ji-Huan He,et al.  Recent development of the homotopy perturbation method , 2008 .

[18]  Mehdi Dehghan,et al.  Inverse problem of diffusion equation by He's homotopy perturbation method , 2007 .

[19]  Mehdi Dehghan,et al.  USE OF HES HOMOTOPY PERTURBATION METHOD FOR SOLVING A PARTIAL DIFFERENTIAL EQUATION ARISING IN MODELING OF FLOW IN POROUS MEDIA , 2008 .

[20]  Mehdi Dehghan,et al.  Solution of the differential algebraic equations via homotopy perturbation method and their engineering applications , 2010, Int. J. Comput. Math..

[21]  M. Dehghan,et al.  The Solution of the Variable Coefficients Fourth-Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method , 2009 .

[22]  Ji-Huan He.  HOMOTOPY PERTURBATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS , 2006 .

[23]  Mehdi Dehghan,et al.  Solution of delay differential equations via a homotopy perturbation method , 2008, Math. Comput. Model..

[24]  Muhammad Aslam Noor,et al.  Homotopy Perturbation Method for Solving Partial Differential Equations , 2009 .

[25]  Ahmet Yildirim,et al.  Application of the homotopy perturbation method for the Fokker–Planck equation , 2010 .

[26]  Ahmet Yildirim,et al.  The Homotopy Perturbation Method for Solving the Modified Korteweg-de Vries Equation , 2008 .

[27]  A Yildirim,et al.  THE HOMOTOPY PERTURBATION METHOD FOR APPROXIMATE SOLUTION OF THE MODIFIED KDV EQUATION , 2008 .

[28]  G. H. Erjaee,et al.  The modified homotopy perturbation method for solving strongly nonlinear oscillators , 2009, Comput. Math. Appl..

[29]  M. Najafi.  Stability treatments of wave system in ℜn with coupling controllers via energy functional and decomposition methods , 2009, Math. Comput. Model..

[30]  M. Najafi.  STUDY OF EXPONENTIAL STABILITY OF COUPLED WAVE SYSTEMS VIA DISTRIBUTED STABILIZER , 2001 .

[31]  Ji-Huan He.  SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[32]  Ahmet Yildirim,et al.  He's homotopy perturbation method for nonlinear differential-difference equations , 2010, Int. J. Comput. Math..

[33]  Mehdi Dehghan,et al.  The numerical solution of the second Painlevé equation , 2009 .

[34]  Yu-Ming Chu,et al.  The homotopy perturbation method for discontinued problems arising in nanotechnology , 2009, Comput. Math. Appl..

[35]  K. Omrani,et al.  Exact solutions for some systems of PDEs by He's homotopy perturbation method , 2011 .

[36]  Mehdi Dehghan,et al.  The solution of coupled Burgers' equations using Adomian-Pade technique , 2007, Appl. Math. Comput..

[37]  K. Noor,et al.  SOLVING SECOND-ORDER SINGULAR PROBLEMS USING HES POLYNOMIALS , 2009 .

[38]  M. Dehghan,et al.  The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique , 2009 .

[39]  Mehdi Dehghan,et al.  On the convergence of He's variational iteration method , 2007 .

[40]  Ahmet Yildirim,et al.  Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method , 2008, Comput. Math. Appl..

[41]  M. Noor,et al.  Traveling Wave Solutions of Seventh-order Generalized KdV Equations Using He's Polynomials , 2009 .

[42]  M. Noor,et al.  Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials , 2008 .

[43]  C. Dang,et al.  An aftertreatment technique for improving the accuracy of Adomian's decomposition method , 2002 .

[44]  G. R. Sarhangi,et al.  Stabilizability of coupled wave equations in parallel under various boundary conditions , 1997, IEEE Trans. Autom. Control..