A numerical method for the solution of singular and singularly perturbed boundary value problems

  • Authors

    • Mohsen Tadi University of Colorado Denver Dept. of Mechanical Engineering
    • Miloje Radenkovic Dept. Of Electrical engineering University of Colorado Denver
    • Yuanlong Wang Graduate student Dept. Of Mechanical Engineering University of Colorado Denver
    2014-08-09
    https://doi.org/10.14419/ijamr.v3i3.3122

  • Abstract

    This note is concerned with a new numerical method for the solution of singular and singularly perturbed boundary value problems. The method uses Fourier sine series and is suitable for Dirichlet-type boundary value problems. It removes the singularity of the problem in a natural way. A number of numerical examples are used to study the applicability of the method.

    Keywords: Dirichlet-type boundary valueproblems, Singular boundary value problems, Singularly perturbed baoundary value problems.

  • References

    1. H.G. Roos, M. Stynes, L. Tobiska, Numerical Methods for singularly perturbed differential equation, Springer-Verlag, (1996).
    2. Bertil Gustafsson, ”A numerical method for solving singular boundary value problems”, Numeri. Math., Vol. 21, (1973), pp. 328-344.
    3. M. Kadalbajoo, V. Agarwal, ”Cubic spline for solving singular two-point boundary value problems”, Applied Mathe- matics and Computation, Vol. 156, (2004), pp. 249-259.
    4. A. Ravi Kanth and Y. Reddy, ”Cubic spline for a class of singular two point boundary value problems”, Applied Mathematics and Computation, Vol. 170, (2005), pp. 733-740.
    5. R.K. Mohanty, P.L. Sachder, N. Jha, ”An O(h4) accurate cubic spline TAGE method for nonlinear singular two point boundary value problem”, Applied Mathematics and Computation, Vol. 158, (2004), pp. 853-868.
    6. V. Shanthi, N. Ramanujam, S. Natesan, ”Fitted mesh method for singularly perturbed Reaction-convection-diffusion problems with boundary and interior layers”, Journal of Applied Mathematics and Computing, Vol. 22, (2006), pp. 49-65.
    7. Randhir Singh, Jitendra Kumar, Gnaneshwar Nelakanti, ”Numerical solution of singular boundary value problems using Greens function and improved decomposition method”, Journal of Applied Mathematics and Computing, Vol. 43, (2013), pp. 409-425.
    8. Isom H. Herron, ”Solving singular boundary value problems for ordinary dierential equations”, Carrib. J. Math. Comput. Sci., Vol. 15, (2013), pp. 1-30.
    9. Fazhan Geng, Minggen Cui, ”Solving singular nonlinear second-order periodic boundary value problems in the repro- ducing kernel space”, Applied Mathematics and Computation, Vol. 192, (2007), pp. 389-398.
    10. Zhiyuan Li, Yulan Wang, Fugui Tan, Xiaohui Wan, Tingfang Nie, ”The Solution of a class of Singularly perturbed two-point boundary value problems by the iterative reproducing kernel method”, Abstract and Applied Analysis, Vol. 2012, (2012), pp. 1-7.
    11. Adel Mohsen, Mohamed El-Gamel, ”On the Galerkin and collocation methods for two-point boundary value problems using Sinc bases”, Computers and Mathematics with Applications, Vol. 56, (2008), pp. 930-941.
    12. M. El Gamel, J. Cannon, ”On the solution of a second-order singularly-perturbed boundary value problem by the Sinc-Galerkin method”, Z. Angew. Math. Phys., Vol. 56, (2005), pp. 45-58.
    13. A. Hamad, M. Tadi, M. Radenkovic, ”A numerical method for singular boundary value problems”, Applied Mathematics and Physics, (2014), to appear.
    14. Manoj Kumar, Yogesh Gupta, ”Methods for solving singualr boundary value problems using splines: a review”, Journal of Applied Mathematics and Computing, Vol. 32, (2010), 265-278.
    15. Aydin Secer, Muhammet Kurulay, ”The Sinc-Galerkin method and its applications on singular Dirichlet-type boundary value problems”, Boundary Value Problems, Vol. 126, (2012), pp. 1-14.

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  • How to Cite

    Tadi, M., Radenkovic, M., & Wang, Y. (2014). A numerical method for the solution of singular and singularly perturbed boundary value problems. International Journal of Applied Mathematical Research, 3(3), 292-300. https://doi.org/10.14419/ijamr.v3i3.3122

    Received date: 2014-07-05

    Accepted date: 2014-08-02

    Published date: 2014-08-09