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Applications of Catalan neural network (CaNN) model

Author

Listed:
  • Merve Güney Duman

    (Department of Engineering Fundamental Science, Sakarya University of Applied Sciences, Sakarya, Türkiye)

  • Sibel Koparal

    (Department of Mathematics, Bursa Uludağ University, Bursa, Türkiye)

  • Ömer Duran

    (Department of Mathematics, Kocaeli University, Kocaeli, Türkiye)

  • NeÅŸe Ömür

    (Department of Mathematics, Kocaeli University, Kocaeli, Türkiye)

Abstract

In this paper, we construct Catalan neural network (CaNN) model and examine the nonlinear solvers of the ordinary nonlinear differential equation using the CaNN model with linear and nonlinear activation functions. Using a single-layer functional linking neural network (FLANN) architecture, we extend input models using the first five Catalan polynomials, update network parameters that we initially randomly select, and use error backpropagation algorithms. The CaNN trial solution for solving nonlinear differential equations is in excellent agreement with the analytical solution. Also, the validity of the CaNN method is investigated by treating second-order differential equations of Lane–Emden type as boundary and initial value problems.

Suggested Citation

  • Merve Güney Duman & Sibel Koparal & Ömer Duran & NeÅŸe Ömür, 2025. "Applications of Catalan neural network (CaNN) model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-17, April.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:04:n:s0129183124502437
    DOI: 10.1142/S0129183124502437
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