@Article{IJNAM-13-1,
author = {J. Deng},
title = {Strong Backward Error Analysis for Euler-Maruyama Method},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {13},
number = {1},
pages = {1--21},
abstract = {<p style="text-align: justify;">Backward error analysis is an important tool to study long time behavior of numerical
methods. The main idea of it is to use perturbed equations, namely modified equations, to represent
the numerical solutions. Since stochastic backward error analysis has not been well developed
so far. This paper investigates the stochastic modified equation and backward error analysis for
Euler-Maruyama method with respect to strong convergence are built up. Like deterministic case,
stochastic modified equations, expressed as formal series, do not converge in general. But there
exists the optimal truncation of the series such that the one step error of the modified equations
is sub-exponentially small with respect to time step. Moreover, the result of stochastic backward
error analysis is used to study the error growth of the Euler-Maruyama method on Kubo oscillator.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/423.html}
}