Numerical approximation for nonlinear stochastic pantograph equations with Markovian switching
作者:
Highlights:
•
摘要
The main aim of the paper is to prove that the implicit numerical approximation can converge to the true solution to highly nonlinear hybrid stochastic pantograph differential equation. After providing the boundedness of the exact solution, the paper proves that the backward Euler–Maruyama numerical method can preserve boundedness of moments, and the numerical approximation converges strongly to the true solution. Finally, the exponential stability criterion on the backward Euler–Maruyama scheme is given, and a high order example is provided to illustrate the main result.
论文关键词:Strong convergence,Polynomial growth conditions,Moment boundedness,Backward Euler–Maruyama method,Markovian switching,Exponential stability
论文评审过程:Received 17 January 2015, Accepted 30 March 2016, Available online 25 April 2016, Version of Record 25 April 2016.
论文官网地址:https://doi.org/10.1016/j.amc.2016.03.040