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 ...

This paper represents a generalization of the stability result on the Euler-Maruyama solution, which is established in the paper M. Milošević, Almost sure exponential stability of solutions to highly ...

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 ...