Numerical Solution of First Passage Problems in Random Vibrations

The reliability of dynamic systems modeled by white noise excited, stochastic, ordinary di erential equations can be computed from deterministic backward Kolmogorov equations. This paper discusses and compares some numerical solution methods for boundary value problems involving backward Kolmogorov equations. The numerical examples concern single degree of freedom oscillators subjected to white noise and ltered white noise excitation. The e ciency of various methods and the sensitivity of the solution to the choice of the numerical parameters are particularly discussed.