English

Stability of analytical solutions and convergence of numerical methods for non-linear stochastic pantograph differential equations

Numerical Analysis 2015-02-03 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1502.00061,
  title  = {Stability of analytical solutions and convergence of numerical methods for non-linear stochastic pantograph differential equations},
  author = {M. H. Song and Y. L. Lu and M. Z. Liu},
  journal= {arXiv preprint arXiv:1502.00061},
  year   = {2015}
}

Comments

12pages