TY - JOUR
T1 - Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument
AU - Chengjian Zhang & Wenjie Shi
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 306
EP - 324
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.150616.071216a
UR - https://global-sci.org/intro/article_detail/eajam/10751.html
KW - Random differential equations, piecewise constant argument, generalised polynomial chaos, finite-dimensional noise, error analysis.
AB - <p style="text-align: justify;">We propose a class of numerical methods for solving nonlinear random differential
equations with piecewise constant argument, called gPCRK methods as they
combine generalised polynomial chaos with Runge-Kutta methods. An error analysis is
presented involving the error arising from a finite-dimensional noise assumption, the
projection error, the aliasing error and the discretisation error. A numerical example is
given to illustrate the effectiveness of this approach.</p>