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A new efficient recursive technique for solving singular boundary value problems arising in various physical models

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Abstract.

The paper deals with a numerical technique for solving nonlinear singular boundary value problems arising in various physical models. First, we convert the original problem to an equivalent integral equation to surmount the singularity and employ afterward the boundary condition to compute the undetermined coefficient. Finally, the integral equation without undetermined coefficient is treated using homotopy perturbation method. The present method is implemented on three physical model examples: i) thermal explosions; ii) steady-state oxygen diffusion in a spherical shell; iii) the equilibrium of the isothermal gas sphere. The results obtained by the present method are compared with that obtained using finite-difference method, B-spline method and a numerical technique based on the direct integration method, and comparison reveals that the proposed method with few solution components produces similar results and the method is computationally efficient than others.

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References

  1. R.K. Pandey, J. Differ. Equ. 127, 110 (1996)

    Article  ADS  Google Scholar 

  2. R.K. Pandey, J. Math. Anal. Appl. 208, 388 (1997)

    Article  MathSciNet  Google Scholar 

  3. R.K. Pandey, Nonlinear Anal. 27, 1 (1996)

    Article  MathSciNet  Google Scholar 

  4. D.L.S. McElwain, J. Theor. Biol. 71, 255 (1978)

    Article  Google Scholar 

  5. H.S. Lin, J. Theor. Biol. 60, 449 (1976)

    Article  Google Scholar 

  6. U. Flesch, J. Theor. Biol. 54, 285 (1975)

    Article  Google Scholar 

  7. B.F. Gray, J. Theor. Biol. 82, 473 (1980)

    Article  Google Scholar 

  8. J.A. Adam, Math. Biosci. 81, 224 (1986)

    Article  Google Scholar 

  9. J.A. Adam, Math. Biosci. 86, 183 (1987)

    Article  Google Scholar 

  10. J.A. Adam, S.A. Maggelakis, Math. Biosci. 97, 121 (1989)

    Article  Google Scholar 

  11. A.C. Burton, Growth 30, 157 (1966)

    Google Scholar 

  12. P.L. Chambre, J. Chem. Phys. 20, 1795 (1952)

    Article  ADS  Google Scholar 

  13. J.B. Keller, J. Rational Mech. Anal. 5, 715 (1956)

    MathSciNet  Google Scholar 

  14. S.V. Parter, SIAM J. Ser. B 2, 500 (1965)

    MathSciNet  Google Scholar 

  15. W.F. Ames, Nonlinear Ordinary Differential Equations in Transport Process (Academia Press, New York, 1968)

  16. M.M. Chawla, C.P. Katti, Numer. Math. 39, 341 (1982)

    Article  MathSciNet  Google Scholar 

  17. M.M. Chawla, J. Comput. Appl. Math. 17, 359 (1987)

    Article  MathSciNet  Google Scholar 

  18. R.K. Pandey, A.K. Singh, Int. J. Comput. Math. 83, 809 (2006)

    Article  MathSciNet  Google Scholar 

  19. R.K. Pandey, A.K. Singh, J. Comput. Appl. Math. 205, 469 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  20. R.K. Pandey, A.K. Singh, J. Comput. Appl. Math. 166, 553 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  21. M.M. Chawla, R. Subramanian, H.L. Sathi, BIT Numer. Math. 28, 88 (1988)

    Article  MathSciNet  Google Scholar 

  22. C.P. Katti, Appl. Numer. Math. 5, 451 (1989)

    Article  MathSciNet  Google Scholar 

  23. R.K. Pandey, Int. J. Comput. Math. 79, 357 (2002)

    Article  MathSciNet  Google Scholar 

  24. H. Caglar, N. Caglar, M. Özer, Chaos Solitions Fractals 39, 1232 (2009)

    Article  ADS  Google Scholar 

  25. M. Abukhaled, S.A. Khuri, A. Sayef, Int. J. Numer. Anal. Modell. 8, 353 (2011)

    Google Scholar 

  26. R. Schreiber, SIAM J. Numer. Anal. 17, 547 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  27. M. Inc, D.J. Evans, Int. J. Comput. Math. 80, 869 (2003)

    Article  MathSciNet  Google Scholar 

  28. N.S. Asaithambi, J.B. Garner, Appl. Math. Comput. 30, 215 (1989)

    Article  MathSciNet  Google Scholar 

  29. J.H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1998)

    Article  ADS  Google Scholar 

  30. G. Adomian, Appl. Math. Lett. 11, 131 (1998)

    Article  MathSciNet  Google Scholar 

  31. M. Danish, S. Kumar, Comput. Chem. Eng. 36, 57 (2012)

    Article  Google Scholar 

  32. S.A. Khuri, A. Sayfy, Math. Comput. Model. 52, 626 (2010)

    Article  MathSciNet  Google Scholar 

  33. A. Janalizadeh, A. Barari, D.D. Ganji, Phys. Lett. A 370, 388 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  34. A.J. Muhammad-Jawad, S.T. Mohyud-Din, World Appl. Sci. J. 7, 96 (2009)

    Google Scholar 

  35. Yu-Xi Wang, Hua-You Si, Lu-Feng Mo, Mathematical problems in Engineering (Hindari Publishing Corporation, 2008) pp. 795--838

  36. S.T. Mohyud-Din, M.A. Noor, Appl. Appl. Math. 3, 224 (2008)

    MathSciNet  Google Scholar 

  37. A. Yildirim, A. Kelleci, World Appl. Sci. J. 7, 84 (2009)

    Google Scholar 

  38. A. Sadighi, D.D. Ganji, Y. Sabzehmeidani, Int. J. Nonlinear Sci. 4, 92 (2007)

    MathSciNet  Google Scholar 

  39. A. Yildirim, S.A. Sezer, Y. Kaplan, Int. J Numer. Methods Fluids 66, 1315 (2010)

    Article  MathSciNet  Google Scholar 

  40. R. Noorzad, A.T. Poor, M. Omidvar, J. Appl. Sci. 8, 369 (2008)

    Article  ADS  Google Scholar 

  41. P. Roul, Appl. and Appl. Math. 5, 1369 (2010)

    MathSciNet  Google Scholar 

  42. Ahmet Yildirim, Int. J. Numer. Methods Heat Fluid Flow 20, 186 (2010)

    Article  Google Scholar 

  43. P. Roul, Commun. Theor. Phys. 60, 269 (2013)

    Article  MathSciNet  Google Scholar 

  44. F. Shakeri, M. Dehghan, Prog. Electromagn. Res. 78, 361 (2008)

    Article  Google Scholar 

  45. P. Roul, P. Meyer, Appl. Math. Modell. 35, 4234 (2011)

    Article  MathSciNet  Google Scholar 

  46. A. Ghobani, J.S. Nadjfi, Int. J. Nonlinear Sci. Numer. Simulat. 8, 229 (2007)

    Google Scholar 

  47. A. Ghorbani, Chaos Solitons Fractals 39, 1486 (2009)

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Visvesvaraya National Institute of Technology, 440010, Nagpur, India

    Pradip Roul

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  1. Pradip Roul
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Roul, P. A new efficient recursive technique for solving singular boundary value problems arising in various physical models. Eur. Phys. J. Plus 131, 105 (2016). https://doi.org/10.1140/epjp/i2016-16105-8

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  • DOI: https://doi.org/10.1140/epjp/i2016-16105-8

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