Chebyshev spectral collocation method for stochastic delay differential equations

Abstract

The purpose of the paper is to propose the Chebyshev spectral collocation method to solve a certain type of stochastic delay differential equations. Based on a spectral collocation method, the scheme is constructed by applying the differentiation matrix DN to approximate the differential operator d/dt. DN is obtained by taking the derivative of the interpolation polynomial PN(t), which is interpolated by choosing the first kind of Chebyshev-Gauss-Lobatto points. Finally, numerical experiments are reported to show the accuracy and effectiveness of the method.