Have a personal or library account? Click to login
Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics Equation Cover

Homotopy Perturbation Algorithm Using Laplace Transform for Gas Dynamics Equation

By: Jagdev Singh,  Devendra Kumar and  Sushila  
Open Access
|Aug 2012

References

  1. A. M. Lyapunov, The General Problem of the Stability of Motion, Taylor & Francis, London, UK, 1992, English translation.10.1080/00207179208934253
  2. J. H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178 (1999), 257-262.10.1016/S0045-7825(99)00018-3
  3. N. H. Sweilam and M. M. Khader, Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method, Computers & Mathematics with Applications, 58 (2009), 2134-2141.10.1016/j.camwa.2009.03.059
  4. J. Saberi-Nadjafi and A. Ghorbani, He's homotopy perturbation method: an effective tool for solving nonlinear integral and integro-differential equations, Computers & Mathematics with Applications, 58 (2009), 1345-1351.10.1016/j.camwa.2009.03.032
  5. A. V. Karmishin, A. I. Zhukov and V. G. Kolosov, Methods of Dynamics Calculation and Testing for Thin-Walled Structures, Mashinostroyenie, Moscow, Russia, 1990.
  6. R. Hirota, Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons, Physical Review Letters, 27 (1971), 1192-1194.10.1103/PhysRevLett.27.1192
  7. A. M. Wazwaz, On multiple soliton solutions for coupled KdV-mkdV equation, Nonlinear Science Letters A, 1 (2010), 289-296.
  8. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Acad. Publ., Boston, 1994.10.1007/978-94-015-8289-6
  9. G. C. Wu and J. H. He, Fractional calculus of variations in fractal spacetime, Nonlinear Science Letters A, 1 (2010), 281-287.
  10. J. H. He, Variational iteration method—a kind of nonlinear analytical technique: some examples, International Journal of Nonlinear Mechanics, 34 (1999), 699-708.10.1016/S0020-7462(98)00048-1
  11. J. H. He and X. H. Wu, Variational iteration method: new development and applications, Computers & Mathematics with Applications, 54 (2007), 881-894.10.1016/j.camwa.2006.12.083
  12. J. H. He, G. C. Wu and F. Austin, The variational iteration method which should be followed, Nonlinear Science Letters A, 1 (2009), 1-30.
  13. L. A. Soltani and A. Shirzadi, A new modification of the variational iteration method, Computers & Mathematics with Applications, 59 (2010), 2528-2535.10.1016/j.camwa.2010.01.012
  14. N. Faraz, Y. Khan and A. Yildirim, Analytical approach to two-dimensional viscous flow with a shrinking sheet via variational iteration algorithm-II, Journal of King Saud University, 23 (2011), 77-81.10.1016/j.jksus.2010.06.010
  15. G. C. Wu and E. W. M. Lee, Fractional variational iteration method and its application, Physics Letters A, 374 (25) (2010), 2506-2509.10.1016/j.physleta.2010.04.034
  16. E. Hesameddini and H. Latifizadeh, Reconstruction of variational iteration algorithms using the Laplace transform, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 1377-1382.
  17. C. Chun, Fourier-series-based variational iteration method for a reliable treatment of heat equations with variable coefficients, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 1383-1388.10.1515/IJNSNS.2009.10.11-12.1383
  18. D. J. Evans and H. Bulut, A new approach to the gas dynamics equation: An application of the decomposition method, Appl. Comput. Math., 79 (7) (2002), 817-822.10.1080/00207160211297
  19. H. Jafari, M. Zabihi and M. Saidy, Application of homotopy perturbation method for solving gas dynamics equation, 2 (48) (2008), 2393-2396.
  20. A. Ghorbani and J. Saberi-Nadjafi, He's homotopy perturbation method for calculating adomian polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 8 (2007), 229-232.10.1515/IJNSNS.2007.8.2.229
  21. A. Ghorbani, Beyond adomian's polynomials: He polynomials, Chaos Solitons Fractals, 39 (2009), 1486-1492.10.1016/j.chaos.2007.06.034
  22. S. T. Mohyud-Din, M. A. Noor and K. I. Noor, Traveling wave solutions of seventh-order generalized KdV equation using He's polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 227-233.10.1515/IJNSNS.2009.10.2.227
  23. Y. Khan and Q. Wu, Homotopy perturbation transform method for nonlinear equations using He's polynomials, Computer and Mathematics with Applications, 61(8) (2011), 1963-1967.10.1016/j.camwa.2010.08.022
  24. S. T. Mohyud-Din and A. Yildirim, Homotopy perturbation method for advection problems, Nonlinear Science Letters A, 1 (2010), 307-312.
  25. J. H. He, Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation, 135 (2003), 73-79.10.1016/S0096-3003(01)00312-5
  26. J. H. He, Comparison of homotopy perturbation method and homotopy analysis method, Applied Mathematics and Computation, 156 (2004), 527-539.10.1016/j.amc.2003.08.008
  27. J. H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation, 151 (2004), 287-292.10.1016/S0096-3003(03)00341-2
  28. J. H. He, Homotopy perturbation method for bifurcation of nonlinear problems, International Journal of Nonlinear Sciences and Numerical Simulation, 6 (2005), 207-208.
  29. J. H. He, Some asymptotic methods for strongly nonlinear equation, International Journal of Modern Physics, 20 (2006), 1144-1199.
  30. J. H. He, Homotopy perturbation method for solving boundary value problems, Physics Letters A, 350 (2006), 87-88.10.1016/j.physleta.2005.10.005
  31. M. Rafei and D. D. Ganji, Explicit solutions of helmhotz equation and fifth-order KdV equation using homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 7 (2006), 321-328.10.1515/IJNSNS.2006.7.3.321
  32. A. M. Siddiqui, R. Mahmood and Q. K. Ghori, Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 7 (2006), 7-14.
  33. D. D. Ganji, The applications of He's homotopy perturbation method to nonlinear equation arising in heat transfer, Physics Letters A, 335 (2006), 337-341.10.1016/j.physleta.2006.02.056
  34. L. Xu, He's homotopy perturbation method for a boundary layer equation in unbounded domain, Computers & Mathematics with Applications, 54 (2007), 1067-1070.10.1016/j.camwa.2006.12.052
  35. J. H. He, An elementary introduction of recently developed asymptotic methods and nanomechanics in textile engineering, International Journal of Modern Physics, 22 (2008), 3487-4578.10.1142/S0217979208048668
  36. J. H. He, Recent developments of the homotopy perturbation method, Topological Methods in Nonlinear Analysis, 31 (2008), 205-209.
  37. E. Hesameddini and H. Latifizadeh, An optimal choice of initial solutions in the homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 1389-1398.
  38. E. Hesameddini and H. Latifizadeh, A new vision of the He's homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 1415-1424.
  39. J. Biazar, M. Gholami Porshokuhi and B. Ghanbari, Extracting a general iterative method from an adomian decomposition method and comparing it to the variational iteration method, Computers & Mathematics with Applications, 59 (2010), 622-628.10.1016/j.camwa.2009.11.001
  40. S. A. Khuri, A Laplace decomposition algorithm applied to a class of nonlinear differential equations, Journal of Applied Mathematics, 1 (2001), 141-155.10.1155/S1110757X01000183
  41. E. Yusufoglu, Numerical solution of Duffing equation by the Laplace decomposition algorithm, Applied Mathematics and Computation, 177 (2006), 572-580.10.1016/j.amc.2005.07.072
  42. Yasir Khan, An effective modification of the Laplace decomposition method for nonlinear equations, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 1373-1376.
  43. Yasir Khan and Naeem Faraz, A new approach to differential difference equations, Journal of Advanced Research in Differential Equations, 2 (2010), 1-12.
  44. S. Islam, Y. Khan, N. Faraz and F. Austin, Numerical solution of logistic differential equations by using the Laplace decomposition method, World Applied Sciences Journal, 8 (2010), 1100-1105.
  45. M. Madani and M. Fathizadeh, Homotopy perturbation algorithm using Laplace transformation, Nonlinear Science Letters A, 1 (2010), 263-267.
  46. S. T. Mohyud-Din, M. A. Noor, K. I. Noor, Traveling wave solutions of seventh-order generalized KdV equation using He's polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 227-233.10.1515/IJNSNS.2009.10.2.227
  47. M. A. Noor, S. T. Mohyud-Din, Variational homotopy perturbation method for solving higher dimensional initial boundary value problems, Mathematical Problems in Engineering 2008 (2008) 11. Article ID 696734, doi:10.1155/2008/696734.10.1155/2008/696734
DOI: https://doi.org/10.2478/v10294-012-0006-2 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180
Language: English
Page range: 55 - 61
Published on: Aug 13, 2012
Published by: University of Ss. Cyril and Methodius in Trnava
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2012 Jagdev Singh, Devendra Kumar, Sushila, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons License.

Volume 8 (2012): Issue 1 (May 2012)