ABSTRACT
This chapter aims to solve differential equations using the functional link artificial neural network (FLANN) model with regression-based weights. It introduces a single-layer Chebyshev polynomial-based FLANN called Chebyshev neural network (ChNN) with regression-based weights to handle first- and higher-order ordinary differential equations (ODEs). The chapter incorporates the structure of the single-layer ChNN model with regression-based weights, its training algorithm, formulation, and gradient computation, respectively. In FLANN, the hidden layer is replaced by a functional expansion block for enhancement of the input patterns using Chebyshev polynomials. So the technique is computationally more efficient than the multilayer perceptron network. ChNN has been successfully applied in system identification, function approximation, digital communication, and solving differential equations. The chapter also utilizes the feed-forward neural network and error back-propagation method for minimizing the error function and modifying the parameters.
