This project explores a novel approach to approximating Euler's Number (e) through fundamental concepts in Geometry and Probability, making it accessible to high school students. Unlike traditional ...

Given an initial value ( y(x_0) = y_0 ), Euler's method approximates the solution of the ODE by stepping forward in small increments. Consider the ODE: [ \frac{dy}{dx} = x + y ] with the initial ...

ABSTRACT: This study is focused on the approximate solution for the class of stochastic delay differential equations. The techniques applied involve the use of Caratheodory and Euler Maruyama ...

This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological ...