A relation between numerical and analytical results for stochastic differential equations
We consider the following simplest ordinary differential equations: the Jacobi equation $y''+K(x)y=0$ with the random coefficient $K(x)=K(x,\omega)$ and the equation $y'=a(x)y$ with the random coefficient $a(x)=a(x,\omega)$. A relation between numerical and analytical approaches to the study of solutions to these equations is examined. The advantages of these approaches are discussed.