Solving Fuzzy Nonlinear Equations Via Stirling’s-Like Method

  • Authors

    • Audu Umar Omesa
    • Mustafa Mamat
    • Ibrahim Mohammed Sulaiman
    • Muhammad Yusuf Waziri
    • Mohamad Afendee Mohamed
    https://doi.org/10.14419/ijet.v7i3.28.27380
  • Stirling’s method, fuzzy nonlinear equations, parametric form, successive substitution.

  • This paper presents a Stirling-like method (SM) for solving fuzzy nonlinear equation, where the SM steps are computed at every iteration. In this method, we combine successive substitution’s and Newton’s method. Numerical experiments with encouraging results are presented that shows the efficiency of the proposed method.

     

     


     

  • References

    1. [1] Ramli, A., Abdullah, M. L., & Mamat, M. (2010). Broyden's method for solving fuzzy nonlinear equations. Advances in Fuzzy Systems, 2010, 1-6.

      [2] Sulaiman, I. M., Mamat, M., & Waziri, M. Y. (2018). Shamanskii method for solving fuzzy nonlinear equation. Proceedings of the 2nd IEEE International Conference on Intelligent Systems Engineering, pp. 1-4.

      [3] Abbasbandy, S., & Asady, B. (2004). Newton's method for solving fuzzy nonlinear equations. Applied Mathematics and Computation, 159(2), 349-356.

      [4] Broyden, C. G. (1965). A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation, 19(92), 577-593.

      [5] Kelley, C. T. (1995). Iterative methods for linear and nonlinear equations. Frontiers in Applied Mathematics, 16, 575-601.

      [6] Waziri, M. Y., & Majid, Z. A. (2012). A new approach for solving dual fuzzy nonlinear equations using Broyden's and Newton's methods. Advances in Fuzzy Systems, 2012, 1-5.

      [7] Dennis Jr, J. E., & Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations. Siam.

      [8] Argyros, I. (2007). Computational theory of iterative methods. Elsevier.

      [9] Abbasbandy, S., & Asady, B. (2004). Newton's method for solving fuzzy nonlinear equations. Applied Mathematics and Computation, 159(2), 349-356.

      [10] Sulaiman, I. M., Mamat, M., Mohamed, M. A., & Waziri, M. Y. (2018). Diagonal updating Shamanskii-like method for solving fuzzy nonlinear equation. Far East Journal of Mathematical Sciences, 103(10), 1619-1629.

      [11] Sulaiman, I. M., Mamat, M., Waziri, M. Y., Fadhilah, A., & Kamfa. K. U. (2016). Regula Falsi method for solving fuzzy nonlinear equation. Far East Journal of Mathematical Sciences, 100(6), 873-884.

      [12] Sulaiman, I. M., Mamat, M., Waziri, M. Y., Mohamed, M. A., & Mohamad, F. S. (2018). Solving fuzzy nonlinear equation via Levenberg-Marquardt method. Far East Journal of Mathematical Sciences, 103(10), 1547-1558.

      [13] Buckley, J. J., & Qu, Y. (1990). Solving linear and quadratic fuzzy equations. Fuzzy Sets and Systems, 38(1), 43-59.

      [14] Kelley, C. T. (1986). A ShamanskiÄ­-like acceleration scheme for nonlinear equations at singular roots. Mathematics of Computation, 47(176), 609-623.

      [15] Sulaiman, I. M., Waziri, M. Y., Olowo, E. S., & Talat, A. N. (2018). Solving fuzzy nonlinear equations with a new class of conjugate gradient method. Malaysian Journal of Computing and Applied Mathematics, 1(1), 11-19.

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  • How to Cite

    Umar Omesa, A., Mamat, M., Mohammed Sulaiman, I., Yusuf Waziri, M., & Afendee Mohamed, M. (2018). Solving Fuzzy Nonlinear Equations Via Stirling’s-Like Method. International Journal of Engineering & Technology, 7(3.28), 335-338. https://doi.org/10.14419/ijet.v7i3.28.27380