Application of Chebyshev neural network to solve Van der Pol equations

  • Authors

    • Sarkhosh Seddighi Chaharborj Department of Mathematics, UPM, Malaysia.Nuclear Science Research School, Nuclear Science and Technology Research Institute (NSTRI), Iran
    • Shahriar S. Chaharborj
    • Phang Pei See
    2021-03-19
    https://doi.org/10.14419/ijbas.v10i1.31431
  • Van der Pol equations, Chebyshev Neural Network, Error back propagation algorithm, Feed forward neural network

  • Abstract

    In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping. The problems of single-well, double-well and double-hump Van der Pol-Dufing equations are studied in this paper. The Chebyshev Neural Network (ChNN) model will be applied to obtain the numerical solutions of these types of equations for the first time. The hidden layer is eliminated by expanding the input pattern by Chebyshev polynomials which employs a single layer neural network. In order to modify the network parameters and to minimize the computed error function, a feed forward neural network model with error back propagation principle is used. The obtained numerical results form the ChNN model will be compared with the analytical solutions, namely Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM), Differential Transform Method (DTM) and exact. Comparisons of the solutions obtained with existing numerical results show that this method is a capable tool for solving this kind of nonlinear problems.

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  • How to Cite

    Seddighi Chaharborj, S., S. Chaharborj, S., & Pei See, P. (2021). Application of Chebyshev neural network to solve Van der Pol equations. International Journal of Basic and Applied Sciences, 10(1), 7-19. https://doi.org/10.14419/ijbas.v10i1.31431

    Received date: 2021-02-05

    Accepted date: 2021-03-03

    Published date: 2021-03-19