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 ...

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 ...

Abstract: This paper introduces two novel methods for solving multi-order fractional differential equations using Bernstein polynomials. The first method, referred to as the fractional operational ...

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 ...

This course is an introduction to the methods of solving ordinary differential equations with an emphasis on applications. We will study the methods of solving first order and second order linear ...

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 ...

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 ...