Collocation methods for stochastic Volterra integro-differential equations with random forcing functions

A Volterra integro-differential equation is said to be stochastic (SVIDE) if it involves any possible combination of (i) random coefficients, (ii) random initial conditions, (iii) random forcing functions, (iv) random kernels. Here stochastic Volterra integro-differential equations are considered with random forcing function of white noise type, and they are solved numerically by collocation methods to obtain sample path solutions. These equations have important applications in physics with the generalized Langevin equation being a representative example. Results of simulations which concern mean estimates of the mean square errors are presented for one example.