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A reliable algorithm for solving tenth-order boundary value problems

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Abstract

In this paper we present an efficient numerical algorithm for solving linear and nonlinear boundary value problems with two-point boundary conditions of tenth-order. The differential transform method is applied to construct the numerical solutions. The proposed algorithm avoids the complexity provided by other numerical approaches. Several illustrative examples are given to demonstrate the effectiveness of the present algorithm.

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References

  1. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Clarendon, Oxford (Reprinted: Dover Books, New York, 1981) (1961)

    MATH  Google Scholar 

  2. Agarwal, R.P.: Boundary Value Problems for Higher Ordinary Differential Equations. World Scientific, Singapore (1986)

    Google Scholar 

  3. Twizell, E.H., Boutayeb, A., Djidjeli, K.: Numerical Methods for eighth, tenth and twelfth-order eigenvalue problems arising in thermal instability. Adv. Comput. Math. 2, 407–436 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Siddiqi, S.S., Twizell, E.H.: Spline solutions of linear tenth order boundary value problems. Int. J. Comput. Math. 68, 345–362 (1998)

    MATH  MathSciNet  Google Scholar 

  5. Siddiqi, S.S., Akram, G.: Solutions of tenth-order boundary value problems using eleventh degree spline. Appl. Math. Comput. 185, 115–127 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Wazwaz, A.M.: The modified Adomian decomposition method for solving linear and nonlinear boundary value problems of tenth-order and twelfth-order. Int. J. Nonlinear Sci. & Numer. Simul. 1, 17–24 (2000)

    MATH  MathSciNet  Google Scholar 

  7. Zhou, J.K.: Differential Transformation and Its Applications for Electrical Circuits (in Chinese). Huazhong University Press, Wuhan, China (1986)

    Google Scholar 

  8. Chen, CK., Ho SH.: Application of differential transformation to eigenvalue problems. Appl. Math. Comput. 79, 173–188 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  9. Chen, C.L., Liu, Y.C.: Solution of two point boundary value problems using the differential transformation method. J. Opt. Theory Appl. 99, 23–35 (1998)

    Article  MATH  Google Scholar 

  10. Jang, M.J., Chen, C.L., Liu, Y.C.: Two-dimensional differential transform for partial differential equations. Appl. Math. Comput. 121, 261–270 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jang, M.J., Chen, C.L., Liu, Y.C.: On solving the initial value problems using the differential transformation method. Appl. Math. Comput. 115, 145–160 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. Jang, M.J., Chen, C.L., Liu, Y.C.: Analysis of the response of a strongly nonlinear damped system using a differential transformation technique. Appl. Math. Comput. 88, 137–151 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  13. Abdel-Halim Hassan, I.H.: On solving some eigenvalue problems by using a differential transformation. Appl. Math. Comput. 127, 1–22 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Abdel-Halim Hassan, I.H.: Chaos, Solitons and Fractals. (in press) doi:10.1016/j.chaos.2006.06.040 (2006)

  15. Ertürk, V.S., Momani, S.: Appl. Math. Comput. (in press), doi:10.1016/j.amc.2006.11.075 (2007)

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, 55139, Samsun, Turkey

    Vedat Suat Erturk

  2. Department of Mathematics, Mutah University, P.O. Box 7, Al-Karak, Jordan

    Shaher Momani

Authors
  1. Vedat Suat Erturk
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  2. Shaher Momani
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Correspondence to Vedat Suat Erturk.

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Erturk, V.S., Momani, S. A reliable algorithm for solving tenth-order boundary value problems. Numer Algor 44, 147–158 (2007). https://doi.org/10.1007/s11075-007-9093-3

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  • DOI: https://doi.org/10.1007/s11075-007-9093-3

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