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 -
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.