TY - JOUR
T1 - A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 192
EP - 208
PY - 2018
DA - 2018/02
SN - 5
DO - http://doi.org/10.4208/eajam.250714.020515a
UR - https://global-sci.org/intro/article_detail/eajam/10794.html
KW - Stochastic differential equation, polynomial chaos, finite difference method, finite element method, non-negative solution.
AB - <p style="text-align: justify;">A numerical comparison of finite difference (FD) and finite element (FE)
methods for a stochastic ordinary differential equation is made. The stochastic ordinary
differential equation is turned into a set of ordinary differential equations by applying
polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical
solutions are all non-negative. When orthogonal polynomials are used for either
continuous or discrete processes, numerical experiments also show that the FE method
is more accurate and efficient than the FD method.</p>