This article deals with the differential computation of sensitivity functions and confidence intervals for model output, when model inputs are subject to systematic or stochastic uncertainties with time-varying variances. The nonlinear, time-varying systems dealt with correspond to the class of nonlinear systems with time-invariant dynamics and boundary conditions involving algebraic-only equations. It is shown that the first-order kernel of a Volterra series expansion of the time-invariant model, allied with a derivation of the algebraic equations, can be used to derive approached differential formulas. These are applied to the case study of a real-size building thermal dynamic model developed with the Clim2000 software; the results are compared with Monte Carlo sampling and show very good agreement.

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