Numerical solutions to linear differential equations on unbounded domain based on ECNN

Abstract

In this paper, we propose a novel single-layer Exponential Chebyshev Neural Network (ECNN) designed to solve ordinary differential equations (ODEs) or systems of ODEs, as well as integro-differential equations (IDEs) or systems of IDEs, defined on infinite domains. We utilize the output of the ECNN as an approximate solution to the original equation and substitute it back into the equation. By employing the ELM (Extreme Learning Machine) algorithm for training, we are able to obtain optimal parameters, thereby deriving a closed-form approximate solution for the original equation. Through a series of numerical experiments, we have verified that the proposed method is both highly effective and robust.