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A Higher Order Implicit Method for Numerical Solution of Singular Initial Value Problems

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Mathematics and Computing (ICMC 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 655))

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Abstract

Recently a lower order implicit method has been presented for solving singular initial value problem. In this article a higher order implicit method has been developed to solve first or higher order problems having an initial singular point. This method is more suitable than second, third and two-stage fourth order implicit Runge-Kutta methods for first order problems. The method also provides significantly better results than the existing lower order implicit method for second order problems.

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References

  1. Chandrasekhar, S.: Introduction to the Study of Stellar Structure. Dover, NewYork (1967)

    Google Scholar 

  2. Davis, H.T.: Introduction to Nonlinear Differential and Integral Equations. Dover, New York (1962)

    Google Scholar 

  3. Richardson, O.U.: The Emission of Electricity from Hot Bodies, London (1921)

    Google Scholar 

  4. Wazwaz, A.M.: A new algorithm for solving differential equations of Lane-Emden type. Appl. Math. Comput. 118, 287–310 (2001)

    MathSciNet  MATH  Google Scholar 

  5. Wazwaz, A.M.: A new method for solving singular initial value problems in the second-order ordinary differential equations. Appl. Math. Comput. 28, 45–57 (2002)

    MathSciNet  MATH  Google Scholar 

  6. Wazwaz, A.M.: The modified decomposition method for analytic treatment of differential equations. Appl. Math. Comput. 173, 165–176 (2002)

    MathSciNet  MATH  Google Scholar 

  7. Wazwaz, A.M.: Adomian decomposition method for a reliable treatment of the Emden-Fowler equation. Appl. Math. Comput. 61, 543–560 (2005)

    MathSciNet  MATH  Google Scholar 

  8. Hasan, Y.Q., Zhu, L.M.: Solving singular initial value problems in the second-order ordinary differential equations. J. Appl. Sci. 7(17), 2505–2508 (2007)

    Article  Google Scholar 

  9. Hasan, Y.Q., Zhu, L.M.: Modified adomian decomposition method for singular initial value problems in the second-order ordinary differential equations. Surv. Math. Appl. 3, 183–193 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Gupta, V.G., Sharma, P.: Solving singular initial value problems of Emden-Fowler and Lane-Amden type. Int. J. Appl. Math. Comput. 1(4), 206–212 (2009)

    Google Scholar 

  11. Demir, H., Sungu, I.C.: Numerical solution of a class of nonlinear Emden-Fowler equations by using differential transform method. J. Arts Sci. 12, 75–82 (2009). Say\(\imath \)/Aral\(\imath \)k

    Google Scholar 

  12. Mukherjee, S., Roy, B., Chaterjee, P.K.: Solution of Lane-Emden equation by differential transform method. Int. J. Nonlinear Sci. 12(4), 478–484 (2011)

    MathSciNet  Google Scholar 

  13. Koch, O., Kofler, P., Weinmuller, E.: The implicit Euler method for the numerical solution of singular initial value problems. Appl. Num. Math. 34, 231–252 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Koch, O., Weinmuller, E.: Analytic and numerical treatment of a singular initial value problem in avalanche modeling. Appl. Math. Comput. 148, 561–570 (2004)

    MathSciNet  MATH  Google Scholar 

  15. Benko, D., Biles, D.C., Robinson, M.P., Spraker, J.S.: Numerical approximation for singular second order differential equations. Math. Comput. Model. 49, 1109–1114 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lakestani, M., Saray, B.N.: Numerical solution of singular IVPs of Emden-Fowler type using Legendre scaling functions. Int. J. Nonlinear Sci. 13(2), 211–219 (2012)

    MathSciNet  MATH  Google Scholar 

  17. Hasan, M.K., Huq, M.A., Rahman, M.S., Rahman, M.M., Alam, M.S.: A new implicit method for numerical solution of singular initial value problems. Int. J. Conceptions Comput. Info Technol. 2(1), 87–91 (2014)

    Google Scholar 

  18. Hasan, M.K., Ahamed, M.S., Alam, M.S., Hossain, M.B.: An implicit method for numerical solution of singular and stiff initial value problems. J. Comput. Eng. 2013, 1–5 (2013). Article ID 720812

    Article  Google Scholar 

  19. Hasan, M.K., Ahamed, M.S., Huq, M.A., Alam, M.S., Hossain, M.B.: An implicit method for numerical solution of second order singular initial value problems. Open Math. J. 7, 1–5 (2014)

    Article  MathSciNet  Google Scholar 

  20. Huq, M.A., Hasan, M.K., Rahman, M.M., Alam, M.S.: A simple and straightforward method for evaluating some singular integrals. Far East J. Math. Edu. 7(2), 93–107 (2011)

    MATH  Google Scholar 

  21. Hasan, M.K., Huq, M.A., Rahaman, M.H., Haque, B.M.I.: A more accurate and straightforward method for evaluating singular integrals. Uni. J. Appl. Math. 3(3), 53–61 (2015)

    Google Scholar 

  22. Balagurusamy, E.: Numerical Methods, 4th edn., pp. 145–171. Tata McGraw-Hill Publishing Company Limited (2004)

    Google Scholar 

  23. Jain, M.K.: Numerical Solution of Differential Equations, 2nd edn., pp. 57–59. Wiley Eastern Limited (1991)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi, 6204, Bangladesh

    M. Kamrul Hasan, M. Suzan Ahamed, M. S. Alam & M. Bellal Hossain

  2. Department of Mathematics, Khulna University of Engineering and Technology, Khulna, 9203, Bangladesh

    B. M. Ikramul Haque

Authors
  1. M. Kamrul Hasan
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  2. M. Suzan Ahamed
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  3. B. M. Ikramul Haque
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  4. M. S. Alam
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  5. M. Bellal Hossain
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Corresponding author

Correspondence to M. Kamrul Hasan .

Editor information

Editors and Affiliations

  1. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  2. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  3. Freie Universität Berlin, Berlin, Germany

    Heinrich Begehr

  4. Fordham University, Bronx, New York, USA

    Mohammad S. Obaidat

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Hasan, M.K., Ahamed, M.S., Haque, B.M.I., Alam, M.S., Hossain, M.B. (2017). A Higher Order Implicit Method for Numerical Solution of Singular Initial Value Problems. In: Giri, D., Mohapatra, R., Begehr, H., Obaidat, M. (eds) Mathematics and Computing. ICMC 2017. Communications in Computer and Information Science, vol 655. Springer, Singapore. https://doi.org/10.1007/978-981-10-4642-1_22

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  • DOI: https://doi.org/10.1007/978-981-10-4642-1_22

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4641-4

  • Online ISBN: 978-981-10-4642-1

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