Comparative analysis of Finite Difference Method (FDM) and Physics-Informed Neural Networks (PINNs)

Abstract

In this analysis, the solutions of the Linear and Non-Linear models are explored and compared using two distinct methods: the Finite Difference Method (FDM) and the Physics-Informed Neural Networks (PINNs). Initially, the solution is derived employing the principles of FDM, followed by solving the same problem using the methodology of PINNs. Subsequently, a comparative examination of the solution graphs with the exact solution is conducted.