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 - <p style="text-align: justify;">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.</p>