Corpus ID: 119301617

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

@inproceedings{MHSong2015StabilityOA,
  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},
  year={2015}
}
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… 

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