Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrodinger-KdV equation
Tóm tắt
In this paper, we apply the homotopy analysis method (HAM) and the homotopy perturbation method (HPM) to obtain approximate analytical solutions of the coupled Schrodinger-KdV equation. The results show that HAM is a very efficient method and that HPM is a special case of HAM.
Tài liệu tham khảo
Batiha, B., Noorani, M.S.M., Hashim, I.: Numerical solution of sine-Gordon equation by variational iteration method. Phys. Lett. A 370, 437–440 (2007)
Fan, E., Hon, Y.C.: Applications of extended tanh method to ‘special’ types of nonlinear equations. Appl. Math. Comput. 141, 351–358 (2003)
Kaya, D., El-Sayed, S.M.: On the solution of the coupled Schrödinger-KdV equation by the decomposition method. Phys. Lett. A 313, 82–88 (2003)
Abdou, M.A., Soliman, A.A.: New applications of variational iteration method. Physica D 211, 1–8 (2005)
Ray, S.: An application of the modified decomposition method for the solution of the coupled Klein–Gordon–Schrodinger equation. Commun. Nonlinear Sci. Numer. Simul. 13, 1311–1317 (2008)
He, J.-H.: Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350, 87–88 (2006)
He, J.-H.: Application of homotopy perturbation method to nonlinear wave equations. Chaos Solitons Fractals 26, 695–700 (2005)
Inc, M., Ugurlu, Y.: Numerical simulation of the regularized long wave equation by He’s homotopy perturbation method. Phys. Lett. A 369, 173–179 (2007)
Momani, S., Noor, M.: Numerical comparison of methods for solving a special fourth-order boundary value problem. Appl. Math. Comput. 191, 218–224 (2007)
Sweilam, N.H.: Variational iteration method for solving cubic nonlinear Schrodinger equation. J. Comput. Appl. Math. 207, 155–163 (2007)
Khuri, S.A.: A new approach to the cubic Schrodinger equation: an application of the decomposition technique. Appl. Math. Comput. 97, 251–254 (1998)
Liao, S.J.: Homotopy analysis method and its application. PhD dissertation, Shanghai Jiao Tong University (1992)
Liao, S.J.: Beyond Perturbation: Introduction to Homotopy Analysis Method. Chapman and Hall/CRC Press, Boca Raton (2003)
Hayat, T., Sajid, M.: On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder. Phys. Lett. A 361, 316–322 (2007)
Abbasbandy, S.: The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys. Lett. A 360, 109–113 (2006)
Liao, S.J.: Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 169, 1186–1194 (2005)
Hayat, T., Khan, M.: Homotopy solutions for a generalized second-grade fluid past a porous plate. Nonlinear Dyn. 42, 395–405 (2005)
Tan, Y., Abbasbandy, S.: Homotopy analysis method for quadratic Riccati differential equation. Commun. Nonlinear Sci. Numer. Simul. 13, 539–546 (2008)
Liao, S.J.: An explicit totally analytic approximation of Blasius viscous flow problems. Int. J. Nonlinear Mech. 34, 759–778 (1999)
Liao, S.J.: On the homotopy anaylsis method for nonlinear problems. Appl. Math. Comput. 147, 499–513 (2004)
Alomari, A.K., Noorani, M.S.M., Nazar, R.: Explicit series solutions of some linear and nonlinear Schrodinger equations via the homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. (2008). doi:10.1016/j.cnsns.2008.01.008
Alomari, A.K., Noorani, M.S.M., Nazar, R.: On the homotopy analysis method for the exact solutions of Helmholtz equation. Chaos Solitons Fractals (2008). doi:10.1016/j.chaos.2008.07.038
Alomari, A.K., Noorani, M.S.M., Nazar, R.: Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system. Commun. Nonlinear Sci. Numer. Simul. (2008). doi:10.1016/j.cnsns.2008.06.011
Alomari, A.K., Noorani, M.S.M., Nazar, R.: Solutions of heat-like and wave-like equations with variable coefficients by means of the homotopy analysis method. Chin. Phys. Lett. 25, 589–592 (2008)
Bataineh, A.S., Alomari, A.K., Noorani, M.S.M., Hashim, I., Nazar, R.: Series solutions of systems of nonlinear fractional differential equations. Acta Appl. Math. (2008). doi:10.1007/s10440-008-9271-x
Liao, S.J.: Series solutions of unsteady boundary-layer flows over a stretching flat plate. Stud. Appl. Math. 117, 239–263 (2006)
Allan, F.M., Syam, M.I.: On the analytic solution of non-homogeneous Blasius problem. J. Comput. Appl. Math. 182, 362–371 (2005)
Abbasbandy, S.: The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation. Phys. Lett. A 361, 478–483 (2007)
Bataineh, A.S., Noorani, M.S.M., Hashim, I.: Solving systems of ODEs by homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 13, 2060–2070 (2008)
Hayat, T., Sajid, M.: On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder. Phys. Lett. A 361, 316–322 (2007)
Sajid, M., Hayat, T., Asghar, S.: Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt. Nonlinear Dyn. 50, 27–35 (2007)