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An efficient method for solving Riccati equation using homotopy perturbation method

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Abstract

In this paper, we propose a new technique to conveniently solve the Riccati equation with both constant and variable coefficients. By combining the transformation of variables with the homotopy perturbation method, this technique possesses a fast convergence rate with high accuracy. We investigate the practicality and efficiency of the technique for several specific examples of the Riccati equation and demonstrate its accuracy by comparing the approximate solution with cases where the exact solution is known.

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References

  1. W T Reid Riccati Differential Equations Chap. 1 Sect. 1 (New York: Academic Press) (1972)

    Google Scholar 

  2. J H He Comput. Methods Appl. Mech. Eng. 178 257 (1999)

    Article  ADS  MATH  Google Scholar 

  3. J H He Non-linear Mech. 35 37 (2000)

    Article  MATH  Google Scholar 

  4. J H He Appl. Math. Comput. 156 527 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. J H He Int. J. NonLinear Mech. 34 699 (1999)

    Article  ADS  MATH  Google Scholar 

  6. J H He Int. J. NonLinear Mech. 35 37 (2000)

    Article  ADS  MATH  Google Scholar 

  7. J H He Appl. Math. Comput. 140 217 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. J H He Therm. Sci. 14 565 (2010)

    ADS  Google Scholar 

  9. J H He Abstr. Appl. Anal. Article ID 857612 (2012)

  10. M J Ablowitz Int. J. Nonlinear Sci. Numer. Simul. 7 399 (2006)

    Google Scholar 

  11. L Cveticanin J. Sound Vib. 285 1171 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. D D Ganji and A Rajabi Int. Commun. Heat Mass Transf. 33 391 (2006)

    Article  Google Scholar 

  13. A A Joneidi, G Domairry and M Babaelahi Commun. Nonlinear Sci. Numer. Simul. 15 3423 (2010)

    Article  ADS  Google Scholar 

  14. D D Ganji and A Sadighi Comput. Appl. Math. 207 24 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. M S H Chowdhury and I Hashim Phys. Lett. A 365 439 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. M S H Chowdhury and I Hashim Phys. Lett. A 368 305 (2007)

  17. M S H Chowdhury and I Hashim Chaos Solitons Fractals. 39 1928 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Z Odibat and S Momani Chaos Solitons Fractals. 36 167 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. S Momani and Z Odibat Phys. Lett. A 365 345 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. S Momani and Z Odibat Comput. Math. Appl. 54 910 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. J Biazar and H Ghazvini Phys. Lett. A 364 79 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  22. H Aminkhah and M Hemmatnezhad Commun. Nonlinear Sci. Numer. Simul 15 835 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  23. D D Ganji Phys. Lett. A 355 337 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. S Abbasbandy Appl. Math. Comput. 173 493 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  25. A M Siddiqui, R Mahmood and Q K Ghori Chaos Solitons Fractals. 35 140 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. J Biazar and H Ghazvini Chaos Solitons Fractals. 39 770 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. M Zare, O Jalili and M Delshadmanesh Indian J. Phys. 86 855 (2012)

    Article  ADS  Google Scholar 

  28. Z Azimzadeh, A R Vahidi and E Babolian Indian J. Phys. 86 721 (2012)

    Article  ADS  Google Scholar 

  29. A Biswas and E V Krishnan Indian J. Phys. 85 1513 (2011)

  30. V Ravichandran, V Chinnathambi and S Rajasekar Indian J. Phys. 83 1593 (2009); ibid., Indian J. Phys. 86 907 (2012)

    Google Scholar 

  31. T Sutradhar, B K Datta and R K Bera Indian J. Phys. 83 1681 (2009)

    Article  ADS  Google Scholar 

  32. S Abbasbandy Appl. Math. Comput. 172 485 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  33. S Abbasbandy Appl. Math. Comput. 175 581 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  34. S Abbasbandy Comput. Appl. Math. 207 59 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Y Tan and S Abbasbandy Commun. Nonlinear Sci. Numer. Simul. 13 539 (2008)

  36. S J Liao Int. J. Nonlinear Mech. 30 371 (1995)

    Article  ADS  MATH  Google Scholar 

  37. J H He Comput. Meth. Appl. Mech. Eng. 178 257 (1999)

    Article  ADS  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Shahr-e-Rey Branch, Islamic Azad University, 18155-144, Tehran, Iran

    A. R. Vahidi

  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, 14778-93855, Tehran, Iran

    Z. Azimzadeh & M. Didgar

Authors
  1. A. R. Vahidi
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  2. Z. Azimzadeh
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  3. M. Didgar
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Corresponding author

Correspondence to A. R. Vahidi.

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Vahidi, A.R., Azimzadeh, Z. & Didgar, M. An efficient method for solving Riccati equation using homotopy perturbation method. Indian J Phys 87, 447–454 (2013). https://doi.org/10.1007/s12648-012-0234-8

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  • DOI: https://doi.org/10.1007/s12648-012-0234-8

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