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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.
Duman et al. (Fri,) studied this question.