Stability of analytical solutions and convergence of numerical methods for non-linear stochastic pantograph differential equations
Provides theoretical guarantees for numerical methods in a specific class of stochastic delay equations, which is incremental for researchers in stochastic differential equations.
The paper establishes polynomial stability conditions for solutions of non-linear stochastic pantograph differential equations and proves convergence of the semi-implicit Euler method, providing orders of consistence and convergence.
In this paper, we study the polynomial stability of analytical solution and convergence of the semi-implicit Euler method for non-linear stochastic pantograph differential equations. Firstly, the sufficient conditions for solutions to grow at a polynomial rate in the sense of mean-square and almost surely are obtained. Secondly, the consistence and convergence of this method are proved. Furthermore, the orders of consistence (in the sense of average and mean-square) and convergence are given, respectively.