Chebyshev neural network model with linear and nonlinear active functions

  • Authors

    • Sarkhosh Seddighi Chaharborj Department of Mathematics, UPM, Malaysia.Nuclear Science Research School, Nuclear Science and Technology Research Institute (NSTRI), Iran
    • Yaghoub Mahmoudi
    2016-09-10
    https://doi.org/10.14419/ijbas.v5i3.6382
  • Lane-Emden equation, Chebyshev Neural Network, Error back propagation algorithm, Feed forward neural network.

  • Abstract

    In this paper the second order non-linear ordinary differential equations of Lane-Emden type as singular initial value problems using Chebyshev Neural Network (ChNN) with linear and nonlinear active functions has been studied. Active functions as, \(\texttt{F(z)=z}, \texttt{sinh(x)}, \texttt{tanh(z)}\) are considered to find the numerical results with high accuracy. Numerical results from Chebyshev Neural Network shows that linear active function has more accuracy and is more convenient compare to other functions.

  • References

    1. [1] S. Chandrasekhar and S. Chandrasekhar. An introduction to the study of stellar structure, volume 2. Courier Dover Publications, 2010.
      [2] H. T. Davis. Introduction to nonlinear differential and integral equations. Courier Dover Publications, 1962.
      [3] H. T. Davis. Introduction to nonlinear differential and integral equations. Courier Dover Publications, 1962.
      [4] L. Dresner. Similarity solutions of nonlinear partial differential equations, volume 88. Pitman London, 1983.
      [5] S. Hoda and H. Nagla. Neural network methods for mixed boundary value problems. International Journal of Nonlinear Science, 11(3):312–316, 2011.
      [6] C. Khalique and P. Ntsime. Exact solutions of the lane–emden-type equation. New Astronomy, 13(7):476–480, 2008.
      [7] S. Mall and S. Chakraverty. Chebyshev neural network based model for solving lane–emden type equations. Applied Mathematics and Computation, 247:100–114, 2014.
      [8] S. Mall and S. Chakraverty. Chebyshev neural network based model for solving lane–emden type equations. Applied Mathematics and Computation, 247:100–114, 2014.
      [9] S. Mall and S. Chakraverty. Numerical solution of nonlinear singular initial value problems of emden–fowler type using chebyshev neural network method. Neurocomputing, 149:975–982, 2015.
      [10] M. S. Mechee and N. Senu. Numerical study of fractional differential equations of lane-emden type by method of collocation. Applied Mathematics, 3:851, 2012.
      [11] E. Momoniat and C. Harley. Approximate implicit solution of a laneemden equation. New Astronomy, 11(7):520–526, 2006.
      [12] A. K. Nasab, A. Kılıc¸man, Z. P. Atabakan, and W. Leong. A numerical approach for solving singular nonlinear lane–emden type equations arising in astrophysics. New Astronomy, 34:178–186, 2015.
      [13] O. P. Singh, R. K. Pandey, and V. K. Singh. An analytic algorithm of lane–emden type equations arising in astrophysics using modified homotopy analysis method. Computer Physics Communications, 180(7):1116–1124, 2009.
      [14] R. A. Van Gorder and K. Vajravelu. Analytic and numerical solutions to the lane–emden equation. Physics Letters A, 372(39):6060–6065, 2008.
      [15] A.-M. Wazwaz. A new algorithm for solving differential equations of lane–emden type. Applied Mathematics and Computation, 118(2):287–310, 2001.

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  • How to Cite

    Seddighi Chaharborj, S., & Mahmoudi, Y. (2016). Chebyshev neural network model with linear and nonlinear active functions. International Journal of Basic and Applied Sciences, 5(3), 182-187. https://doi.org/10.14419/ijbas.v5i3.6382

    Received date: 2016-06-19

    Accepted date: 2016-07-25

    Published date: 2016-09-10