TY - JOUR T1 - Strong Predictor-Corrector Methods for Stochastic Pantograph Equations AU - Xiao , Feiyan AU - Wang , Peng JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 11 PY - 2016 DA - 2016/02 SN - 34 DO - http://doi.org/10.4208/jcm.1506-m2014-0110 UR - https://global-sci.org/intro/article_detail/jcm/9779.html KW - Stochastic pantograph equation, Predictor-corrector method, MS-convergence, MS-stability. AB -

The paper introduces a new class of numerical schemes for the approximate solutions of stochastic pantograph equations. As an effective technique to implement implicit stochastic methods, strong predictor-corrector methods (PCMs) are designed to handle scenario simulation of solutions of stochastic pantograph equations. It is proved that the PCMs are strong convergent with order $\frac{1}{2}$. Linear MS-stability of stochastic pantograph equations and the PCMs are researched in the paper. Sufficient conditions of MS-unstability of stochastic pantograph equations and MS-stability of the PCMs are obtained, respectively. Numerical experiments demonstrate these theoretical results.