Mean-Square Stability of Milstein Methods for Stochastic Pantograph Equations

Abstract EN

This paper deals with nonlinear stochastic pantograph equations.

For solving the equations, a class of extended Milstein methods are suggested.

A mean-square stability criterion for this type of equations is presented.

It is proved that under the suitable conditions the Milstein methods preserve the mean-square stability.

Numerical examples further illustrate the obtained theoretical results.