Mean-square stability of second-order Runge–Kutta methods for multi-dimensional linear stochastic differential systems

A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems

We are concerned with a linear mean-square stability analysis of numerical methods applied to systems of stochastic differential equations (SDEs) and, in particular, consider the θ-Maruyama and the θ-Milstein method in this context. We propose a technique, based on the vectorisation of matrices and the Kronecker product, to deal with the matrix expressions arising in this analysis and provide t...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Mean Square Stability of Impulsive Stochastic Differential Systems

Effective order strong stability preserving RungeKutta methods

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of ef...

On exponential mean-square stability of two-step Maruyama methods for stochastic delay differential equations

We are concerned with the exponential mean-square stability of two-step Maruyama methods for stochastic differential equations with time delay. We propose a family of schemes and prove that it can maintain the exponential mean-square stability of the linear stochastic delay differential equation for every step size of integral fraction of the delay in the equation. Numerical results for linear ...