In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly ...

The object of this work is to describe how to implement the differential ‎transformation method (DTM) for finding exact and approximate solutions of ‎the second-order random differential equations. To ...

Abstract: Physics-informed neural networks (PINNs) offer a flexible framework for solving differential equations using physical constraints and data. This study focuses on second-order ...

This Python code provides a framework for solving non-linear or linear differential equations using neural networks, specifically using the PyTorch library. Additionally, it includes a class that ...

Abstract: Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...