A stochastic collocation method for stochastic Volterra equations of the second kind

Abstract

This work describes and analyzes a stochastic collocation method for stochastic Volterra integral equations (SVIEs) of the second kind with random forcing terms. A collocation method is used in temporal direction, and a spectral collocation method is used in the stochastic dimension, which lead to an uncoupled linear system associated with the collocation points. The convergence analysis is carried out and the optimal error estimates are obtained. Numerical experiments are conducted to verify the error estimates and demonstrate the effectiveness of the proposed numerical method.