Year 2011,
Volume 01,
Issue 1,
27 - 34,
01.06.2011
M. KAZEMİ-SANGSEREKİ
D. D. GANJİ
M. GORJİ-BANDPY
References
- Evans, D.J. and Bulut, H., (2002), A New approach to the gas dynamics equation: An Application of the Decomposition method. Intern. J. Computer Math., vol.79(7).
- He, J. H., (2004), The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation, 151, 287-292.
- Siddiqui, A.M., Mahmood, R. and Ghori, Q.K., (2006), Thin film flow of a third grade fluid on a moving belt by Hes homotopy perturbation method, Internat J. Nonlinear Sci. Numer. Simul, 7(1), 714.
- Abbasbandy, S., (2006), Iterated Hes homotopy perturbation method for quadratic Riccati differential equation, Appl. Math. Comput., 175, 581-589.
- Ganji, J. D. D. and Sadighi, A., (2006), Application of Hes Homotopyprturbation Method to Nonlin- ear Coupled Systems of Reactiondiffusion Equations, International Journal of Nonlinear Science and Numerical Simulation, 7(4), 411-418.
- Rafei, M. and Ganji, D. D., (2006), Explicit Solutions of Helmholtz Equation and Fifthorder Kdv Equation using Homotopyperturbation Method, Int. J. Nonl. Sci. and Num. Simu., 7(3), 321-328.
- Ganji, D. D. and Rajabi, A., (2006), Assessment of homotopy-perturbation and perturbation merhods in heat radiation equations, Internat. Comm. Heat Mass Transfer, 33, 391-400.
- He, J.H., (1999), Homotopy perturbation technique, J. Comput. Math. Appl. Mech. Eng., 17(8), 257-262.
- He, J.H., (2000), A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Non-Linear Mech., 351, 37-43.
- He, J.H., (2005), Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals, 26(3), 695-700.
- He, J.H., (2006), Homotopy perturbation method for solving boundary value problems, Physics Letter A, 350(12), 87-88.
- Khaleghi, H., Ganji, D. D. and Sadighi, A., (2007), Application of variational iteration and Homotopy- perturbation methods to nonlinear heat transfer equations with variable coefficients, Numerical Heat Transfer, Part A, 52(1), 25-42.
- He, J.H., (2006), New interpretation of Homotopy perturbation method. Int. J. Mod. Phys. B, 20(18), 2561-2568.
- Sadighi, A. and Ganji, D. D, (2007), Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods, International Journal of Nonlinear Science and Numerical Simulation, 8(3), 435-444.
- Ganji, D. D. and A. Sadighi, (2007), Application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, Journal of Computational and Applied mathematics, 207, 24-34.
- He, J.H., (1999), Variational iteration method kind of non-linear analytical technique: some examples, Internat. J. Nonlinear Mech., 34(4), 699-708.
- He, J.H., (2000), Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation, 114, 115-123.
- Abdou, M. A. and Soliman, A.A., (2005), Variational iteration method for solving Burgers and coupled Burgers equations, J. Comput. Appl. Math., 181(2), 245-252.
- Wazwaz, A. M., (2006), The variational iteration method for rational solutions for KdV, K(2,2) Burgers, and cubic Boussinesq equations, J. Comput. Appl. Math., in press.
- Sweilam, N. H. and Khader, M. M., (2007), Variational iteration method for one dimensional nonlinear thermoelasticity. Chaos Soliton Fract., 32, 145-149.
- Abbasbandy, S., (2006), Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomians decomposition method, Appl. Math. Comput.,172, 485-490.
- Wazwaz, A.M., (2006), A comparison between the variational iteration method and Adomian decom- position method, J. Comput. Appl. Math., in press.
- Biazar, J., Babolian, E. and Islam, R., (2004), Solution of the system of ordinary differential equations by Adomian decomposition method, Applied Mathematics and Computation, 147, 713-719.
APPLICATION OF THE HOMOTOPY PERTURBATION METHOD HPM AND VARIATIONAL ITERATION METHOD VIM TO GAS DYNAMIC EQUATION
Year 2011,
Volume 01,
Issue 1,
27 - 34,
01.06.2011
M. KAZEMİ-SANGSEREKİ
D. D. GANJİ
M. GORJİ-BANDPY
Abstract
A gas-dynamic control system is one where the path of an object in flight is controlled by either the generation or redirection of gas flow out of an orifice rather than with the traditional movable control surfaces. In this paper considering Hes Homotopy perturbation and Variational iteration methods are calculated the homogeneous gas dynamics equations. The exact analytic solution of the equation is calculated in the form of a series with easily computable components like to Adomians decomposition method. The Comparison of result of HPM and VIM with Adomians decomposition method show that they are agreement with them, and HPM, VIM can solve large class of nonlinear problems
References
- Evans, D.J. and Bulut, H., (2002), A New approach to the gas dynamics equation: An Application of the Decomposition method. Intern. J. Computer Math., vol.79(7).
- He, J. H., (2004), The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation, 151, 287-292.
- Siddiqui, A.M., Mahmood, R. and Ghori, Q.K., (2006), Thin film flow of a third grade fluid on a moving belt by Hes homotopy perturbation method, Internat J. Nonlinear Sci. Numer. Simul, 7(1), 714.
- Abbasbandy, S., (2006), Iterated Hes homotopy perturbation method for quadratic Riccati differential equation, Appl. Math. Comput., 175, 581-589.
- Ganji, J. D. D. and Sadighi, A., (2006), Application of Hes Homotopyprturbation Method to Nonlin- ear Coupled Systems of Reactiondiffusion Equations, International Journal of Nonlinear Science and Numerical Simulation, 7(4), 411-418.
- Rafei, M. and Ganji, D. D., (2006), Explicit Solutions of Helmholtz Equation and Fifthorder Kdv Equation using Homotopyperturbation Method, Int. J. Nonl. Sci. and Num. Simu., 7(3), 321-328.
- Ganji, D. D. and Rajabi, A., (2006), Assessment of homotopy-perturbation and perturbation merhods in heat radiation equations, Internat. Comm. Heat Mass Transfer, 33, 391-400.
- He, J.H., (1999), Homotopy perturbation technique, J. Comput. Math. Appl. Mech. Eng., 17(8), 257-262.
- He, J.H., (2000), A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Non-Linear Mech., 351, 37-43.
- He, J.H., (2005), Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals, 26(3), 695-700.
- He, J.H., (2006), Homotopy perturbation method for solving boundary value problems, Physics Letter A, 350(12), 87-88.
- Khaleghi, H., Ganji, D. D. and Sadighi, A., (2007), Application of variational iteration and Homotopy- perturbation methods to nonlinear heat transfer equations with variable coefficients, Numerical Heat Transfer, Part A, 52(1), 25-42.
- He, J.H., (2006), New interpretation of Homotopy perturbation method. Int. J. Mod. Phys. B, 20(18), 2561-2568.
- Sadighi, A. and Ganji, D. D, (2007), Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods, International Journal of Nonlinear Science and Numerical Simulation, 8(3), 435-444.
- Ganji, D. D. and A. Sadighi, (2007), Application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, Journal of Computational and Applied mathematics, 207, 24-34.
- He, J.H., (1999), Variational iteration method kind of non-linear analytical technique: some examples, Internat. J. Nonlinear Mech., 34(4), 699-708.
- He, J.H., (2000), Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation, 114, 115-123.
- Abdou, M. A. and Soliman, A.A., (2005), Variational iteration method for solving Burgers and coupled Burgers equations, J. Comput. Appl. Math., 181(2), 245-252.
- Wazwaz, A. M., (2006), The variational iteration method for rational solutions for KdV, K(2,2) Burgers, and cubic Boussinesq equations, J. Comput. Appl. Math., in press.
- Sweilam, N. H. and Khader, M. M., (2007), Variational iteration method for one dimensional nonlinear thermoelasticity. Chaos Soliton Fract., 32, 145-149.
- Abbasbandy, S., (2006), Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomians decomposition method, Appl. Math. Comput.,172, 485-490.
- Wazwaz, A.M., (2006), A comparison between the variational iteration method and Adomian decom- position method, J. Comput. Appl. Math., in press.
- Biazar, J., Babolian, E. and Islam, R., (2004), Solution of the system of ordinary differential equations by Adomian decomposition method, Applied Mathematics and Computation, 147, 713-719.