The numerical solution of random initial-value problems

We outline a numerical technique for the solution of systems of nonlinear ordinary differential equations containing arbitrary numbers of random parameters and random initial conditions. The random parameters are restricted to be time-independent, and hence, stochastic processes are excluded from consideration. Depending upon the number of random initial conditions and parameters relative to the number of dependent variables, this technique yields either the joint probability density function for the dependent variables or the marginal probability density functions for individual dependent variables.