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.