Numerical Solution Of Stochastic Differential Equations Using Moving Least Squares

This paper investigates numerical solution of stochastic differential equations by applying moving least squares approximation in a stochastic Galerkin projection scheme. Two different types of probability distribution functions studied here are uniform and lognormal. Numerical solution of problems with uniform random inputs are compared with Legendrebase polynomial chaos expansion. In the case of lognormal distribution, (modified) Gram-Schmidt polynomial is used for comparison. In different examples it is demonstrated that the accuracy of moving least squares is comparable with the ones of Legendre-chaos expansion and Gram-Schmidt.